arXiv Daily Digest - 2026-05-08

Quantum thermalization describes how interacting quantum systems relax toward thermal equilibrium, a central problem in modern physics. Yet most experimental information on many-body systems comes from short-time transition spectroscopy, typically interpreted within Kubo's linear-response framework. These perspectives - long-time equilibration versus short-time response - seem fundamentally disconnected. Here we establish an exact link between them: the Kubo-Thermalization correspondence, which connects long-time thermalized magnetization under weak driving to short-time linear-response spectra for a spin coupled to a thermal bath. The correspondence holds even when the steady state differs substantially from the initial state and when each regime is individually difficult to describe theoretically. We experimentally confirm the correspondence using effective spin-1/2 impurities realized with ultracold fermions in two internal states coupled to a Fermi sea. Our results provide a rare exact statement about quantum thermalization and offer a novel route to infer thermalization dynamics from equilibrium response measurements in strongly interacting quantum systems, independent of microscopic details of the system-bath coupling.

Many astronomical surveys prompt follow-up observations, but the decision process through which candidates are selected for follow-up can be difficult to model. This poses a challenge when inferring properties of the intrinsic population of astrophysical sources, rather than those of the set of objects detected by the survey and often-incomplete follow-up observations. We alleviate this problem by demonstrating that explicitly modeling of the follow-up selection process is not required for self-consistent inference of the intrinsic population. Using the framework of hierarchical Bayesian inference, we show that the intrinsic population can be accurately inferred even when the decision to follow up candidates strongly correlates with latent parameters of interest. We provide several worked examples, showing that the precision of posterior constraints can depend on the follow-up process and that one may have to model a population of contaminants if the initial selection is imperfect. Our result could dramatically simplify population inference that incorporates uncoordinated follow-up from multiple observers triggered by the deluge of candidates from surveys like LSST, Gaia, and next-generation gravitational-wave interferometers.

Machine learning nowadays becomes a useful instrument in many subjects. In this paper we use interpretable machine learning to build quantum algorithm. By studying the parameters of the machine learning algorithm we were able to construct universal shortest analytic quantum algorithm for arbitrary diagonal matrix of any size.

In this review, we establish the mathematical framework of geometrothermodynamics (GTD) as a formalism capable of describing non-extensive, quasi-homogeneous, self-gravitating systems in a Legendre-invariant manner. We argue that the fundamental equations of black holes are quasi-homogeneous functions, a property that invalidates the standard Euler identity of laboratory thermodynamics. We derive the metrics for the equilibrium manifold and analyze their curvature singularities for the Reissner-Nordström, Kerr, and Kerr-Newman black holes. Furthermore, we establish a direct correspondence between the curvature singularities of the equilibrium space and phase transitions, as determined by the divergences of the corresponding heat capacities.

Matrix product states provide efficient classical descriptions of quantum systems that may be useful as reference states for quantum algorithms such as quantum phase estimation and quantum-selected configuration interaction. Shallow circuit constructions for loading matrix product states onto quantum computers is necessary for this to be practical on near-term hardware. We present a decomposition of matrix product states to log-depth quantum circuits via a simple tree tensor network renormalisation procedure. Our method exposes an explicit parameter which can be used to trade a small amount of fidelity for large savings in circuit depth. We extend this decomposition to the case of matrix product operators allowing us to construct log-depth and ancilla-free circuits to calculate overlaps of the form $\left |\langleφ|U|ψ\rangle\right |^2$. In particular, we demonstrate an interpretation of these circuits as \emph{verifier circuits} with application to circuit-level device calibration.

The Schrödinger--Newton (SN) equation provides a semiclassical framework for the evolution of self-gravitating of massive quantum systems. We propose a two-body Schrödinger--Newton model that separates local nonlinear self-localization from the nonseparable Newtonian pair potential. Analytically, we show that the nonlinear self-field preserves the Schmidt spectrum, whereas direct entanglement generation arises from the nonseparable pair potential. Using numerical simulations in a regularized one-dimensional geometry, we find that entanglement generation depends sensitively on the initial spatial configuration and on the mass ratio. Highly localized, self-bound wavepackets experience minimal entanglement growth during scattering. Spatial delocalization and kinetic dispersion broaden the interaction region, amplifying the entangling power of the pair potential and exciting higher-order spatial modes. For dispersive Gaussian initial states, mass asymmetry shatters the lighter particle, producing Wigner negativity and rapid entanglement growth, whereas stationary SN profiles strongly suppress this effect. Stationary SN profiles isolate the bare pair-potential contribution; dispersive Gaussian initial states inflate it.

We present a constructive framework for designing transformations between structured light fields using birefringent optical elements, formulated in terms of SU(2) operations on polarization. Within this framework, transformations between vector beams are treated as spatially varying SU(2) operations, leading to a direct procedure for designing doubly inhomogeneous waveplates (d-plates) that implement the desired mapping. We identify a condition under which a single element implements a prescribed transformation exactly, including the global phase, and provide an explicit prescription for constructing the corresponding doubly inhomogeneous waveplate (d-plate) when this condition is satisfied, along with its realization using a finite sequence of singly inhomogeneous plates, including a QHQ configuration. Within this formulation, a broad class of problems in structured light can be treated within a single framework, including vector beam transformations, spin-orbital dynamics, and complex beam shaping. Crucially, the same SU(2) operations directly realize quantum channels on the orbital angular momentum degree of freedom, with polarization serving as a physical ancilla. These results establish a unified and explicitly constructive route to complex beam shaping and vector beam transformations based on SU(2) parameter synthesis, and provide a systematic foundation for designing next-generation photonic elements for structured light and spin-orbit information processing.

Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show that appending linearly independent rows to a check matrix of a stabilizer code can reduce the search space for a valid degenerate solution. Motivated by this, we extend the recently proposed affine subcode ensemble decoding technique from the classical to the quantum setting. Moreover, we employ overcomplete matrices for each decoding path. Monte-Carlo simulations on toric and generalized bicycle codes demonstrate improved convergence and reduced logical error rate.

Using Schwinger-Keldysh field theory (SKFT), we engineer a dissipative and driven (i.e., out of equilibrium) bosonic bath acting on classical localized spins within a ferromagnetic insulator (FI) layer whose dynamics is governed by the Landau-Lifshitz-Gilbert equation, as is usually assumed in spintronics and magnonics. The bosonic bath is comprised of quantum magnons within a layer of altermagnetic insulator (AMI) that is attached to a conventional FI layer, often one of the key ingredients within spintronic and magnonic multilayers, so that interaction between slow classical (in the FI layer) and fast quantum (in the AMI layer) localized spins ensues. Such a bath, including its driving to produce a nonequilibrium distribution of altermagnetic magnons, generates a rich structure of the SKFT-derived extended LLG equation for classical spins within the FI layer. Our LLG equation contains two damping terms, both of which are spatially nonlocal and anisotropic, while one of them is also intrinsically non-Markovian, i.e., nonlocal in time. We demonstrate how to exploit these terms for tuning spintronic and magnonic effects within the FI layer of AMI/FI bilayers that involve spin wave or domain wall propagation, as well as skyrmion annihilation.

Data-processing inequalities capture the phenomenon that two probability distributions can only become less distinguishable under any common post-processing. For more fine-grained inequalities, one turns to strong data-processing inequality (SDPI) constants, which give the strongest inequalities for a given channel and reference state for a fixed measure of distinguishability. These quantities have been used to quantify the rate at which time-homogeneous Markov chains contract towards a fixed point both in the classical and quantum setting. In this work, we establish that quantum $f$-divergences satisfy a local reverse Pinsker inequality, which implies the asymptotic contraction rate of a primitive channel to its stationary state is upper bounded by the SDPI constant of any non-commutative $χ^2$-divergence. Using quantum-detailed balance, we establish a sufficient condition for these bounds to be tight. Finally, we apply these results to Petz, Matsumoto, and Hirche-Tomamichel $f$-divergences, establishing new and strengthening previously known results.

Universality and scaling are hallmarks of second-order phase transitions but are generally unexpected in first-order quantum phase transitions (FOQPTs). We present a microscopic theory showing that quantum criticality can emerge around the quantum spinodal point of FOQPTs where metastability disappears. We demonstrate that, at this instability, resonant local excitations dynamically decouple a Hilbert subspace characterized by an emergent discrete translational symmetry. Projecting the original Hamiltonian onto this subspace yields an effective Hamiltonian that exhibits a genuine second-order quantum phase transition (SOQPT) and the Kibble-Zurek scaling. We validate this framework in the tilted Ising chain which breaks Z_2 symmetry, and predict the absence of criticality in the staggered-field PXP model. This work indicates that the FOQPT dynamics is usually governed by an emergent critical point around the quantum spinodal point. Our study establishes a bridge between the dynamics of the FOQPT and SOQPT, and thus sheds new light on the long-standing conundrum of the dynamics of the FOQPT.

In this work, we revisit the idea of using an interferometer of pairs of Josephson junctions as a protected rhombus qubit. Unlike in the original proposal, where the qubit states are encoded into odd and even parity charge states, here, we intentionally alter the energy of one of the junctions to investigate the soft version of the rhombus qubit. This approach allows us to directly probe the qubit transitions over several GHz and reduce the potential drawbacks of the interferometer-based protection. Away from a half flux quantum external field, the large shunting capacitors of the circuit ensure localized qubit states in different phase valleys, leading to a biased-noise qubit. In the realized circuit, we measure an average $T_1\approx500\,μ$s relaxation time in the biased-noise regime (with a Ramsey dephasing time of $T^{R}_\varphi\approx90\,$ns), while an average $T_1\approx27\,μ$s relaxation time at frustration (with $T^{R}_\varphi\approx670\,$ns). Our loss analysis on this multi-mode circuit indicates that at low frequencies, flux noise and quasiparticle tunneling limit the relaxation times, pointing toward the presence of an optimal operating regime of around a few GHz.

We investigate the presence of memory in the sequential measurement statistics of an open quantum system, as witnessed by the departure from the quantum regression theorem (QRT), that is, the possibility to predict multitime probabilities from the one-time reduced dynamical map. For factorized initial states, we identify an exact decomposition of the two-time propagator into a QRT-like contribution, fully determined by the reduced dynamical map, and a memory term encoding system--environment correlations across the intervention; in the weak-coupling regime, the memory term yields an explicit second-order correction expressed in terms of the reduced map and bath correlation functions. Furthermore, we introduce an operational quantifier of QRT violations based on the distance between exact and QRT-predicted joint probabilities. Benchmarking the framework on a spin--boson model and using a pseudomode embedding as nonperturbative reference, we comprehensively analyze the impact of spectral-density parameters, environmental temperature, and measurement protocols on the non-Markovianity of the multitime statistics. Comparison with a one-time quantifier shows that reduced-state non-Markovianity and multitime memory are related but inequivalent: the latter, as probed through sequential statistics, is intrinsically protocol dependent and can become visible at higher temporal order even when two-time statistics remain compatible with QRT predictions.

Non-radial oscillation modes of neutron stars serve as diagnostics of their internal composition and relativistic structure. In this work, we investigate the perturbations of static and spherically symmetric neutron stars characterized by an anisotropic pressure. Given the background symmetry, perturbations decouple into polar and axial modes. To date, axial modes have remained less explored, primarily because matter and metric perturbations decouple in the isotropic limit. In this work, we provide a consistent treatment of axial modes and demonstrate that pressure anisotropy induces a direct coupling between matter and metric perturbations. We employ parameterized anisotropy models that ensure consistency with the treatment of matter perturbations. We numerically integrate the linearized Einstein field equations for the axial modes, employing a diverse set of realistic equations of state. Our results indicate that as the stellar mass grows, the frequency of the lower $w$-mode generally decreases, while its damping time increases. Softer equation of states typically yield slightly higher oscillation frequencies. Furthermore, larger anisotropy (i.e., when the tangential pressure exceeds the radial pressure) allows for more massive equilibrium configurations, which correspondingly leads to lower oscillation frequencies and prolonged damping times. Finally, we demonstrate that the frequency and damping time, both scaled by the stellar mass, exhibit a nearly universal quadratic dependence on the stellar compactness, remaining largely insensitive to both the underlying equation of state and the specific anisotropy model.

Quantum linear-system algorithms (QLSAs) have rigorous worst-case complexity guarantees, but their runtimes are often chosen from spectral information assumed in advance. What is largely lacking is an a posteriori progress flag: most QLSA workflows, unlike the classical counterparts, do not provide a built-in mechanism to signal whether a particular instance has already converged. For discretizations of elliptic PDEs $-\nabla\cdot(a(x)\nabla u(x))=f(x),$ with divergence--gradient structure \[ -\nabla\cdot \big(a(x)\nabla) \approx A_h=G_h^\dagger G_h, \] we formulate a stable first-order ODE whose limiting solution block is the desired Galerkin solution. The PDE-dependent scale is then \(\norm{G_h}=\bigO(h^{-1})\), comparable to factorized QLSA constructions with square-root condition-number scaling. We design an augmented dynamics with residual variables, in which measuring a residual register gives an on-the-fly convergence indicator without reconstructing the solution vector. For smooth right-hand sides, dynamic stopping can reduce the evolution time and gate count relative to a fixed worst-case schedule, and may also reduce exposure to accumulated hardware errors. Numerical experiments for a two-dimensional finite element Poisson problem show that the residual-register probability follows the actual error decay and, for some right-hand sides, can stop the quantum circuit well before a conservative worst-case runtime estimate is reached.

We study the large-$c$ expansion of general relativity in ADM variables. Using a unified even $ω$-expansion, the ADM formulation gives a common starting point for Galilean and Carrollian limits. We focus on the Galilean branch and derive the ADM action and field equations up to NNLO. We then construct stationary vacuum solutions in weak and strong branches. In the weak branch, we find NLO Kerr-type, Hartle-Thorne-type and mixed-type solutions. The NLO weak equations also allow a simple extension to higher mass multipoles. At NNLO, the weak Kerr-type and extended Hartle-Thorne-type sectors solve the equations separately, but their naive sum is not a solution. The nonlinear NNLO equations generate mixed $J^2Q$ source terms, which require additional corrections to the NNLO lapse and NNLO spatial tensor field. This gives a mixed weak-branch Galilean solution in the ADM gauge. In the strong branch, Kerr-type data solve the equations through NNLO while the strong Hartle-Thorne-type data solve the NLO equations. We also explain how the ADM data can be reconstructed into approximate spacetime metrics. Since these metrics include spin, quadrupole and mixed spin-quadrupole effects, they may be useful for studying the spacetime around rotating compact objects such as black holes and neutron stars.

The growing computational demands of classical neural networks have intensified the search for energy-efficient and powerful computational alternatives. Quantum neural networks (QNNs) implemented on integrated photonic platforms offer a compelling avenue, offering exceptional computational power enhancements, with inherent programmability and scalability of integrated architectures. A critical challenge, however, is implementing the fundamental non-unitary and nonlinear activation function of QNNs within a linear quantum photonic system. Existing strategies, such as the adding ancillary qubits and measurement-based feedback or forward are constrained by high qubit resource costs, overhead devices, and poor cascadability. Here, we propose a novel deep photonic QNN with an expanded computational Hilbert space via input replication and mode expansion, which enables the realization of effective non-unitary and nonlinear activation on a linear programmable quantum photonic chip. This approach eliminates the need for physical ancillary qubits, measurement-induced qubit consumption and the measurement device burden, thereby significantly reduce resource costs. The fabricated chip integrates four high-quality entanglement sources and a programmable high-dimensional interferometric network, enabling a two-hidden-layer QNN that exhibits dimension-enhanced expressivity over the existing QNN architectures. We demonstrate its capabilities across diverse tasks, including nonlinear classification, image generation, and quantum Gibbs state preparation. This work establishes a scalable and efficient architecture toward practical quantum deep learning systems capable of tackling problems beyond the reach of classical computation.

The non-linear nature of Yang-Mills theory presents a challenge for extracting exact classical solutions, which are useful for understanding non-perturbative vacuum structures. In this paper, an algebraic tensor ring decomposition framework is introduced to systematically map the non-linear partial differential equations (PDEs) of Yang-Mills theory into tractable differential-algebraic systems. By promoting static pure-gauge backgrounds to dynamical variables, the reference state acts as a geometric template whose Maurer-Cartan forms generate the algebraic cross-terms necessary to stabilize non-linear self-interactions. To analytically resolve the resulting differential ideals, specific differential-algebraic quotient rings are employed as evaluation tools, and the solution space is organized by an algebraic bifurcation analysis. Applying this framework, three distinct classes of exact solutions are extracted: (i) relativistic $SU(2)$ color waves evaluated over an elliptic quotient ring, where the differential ideal bifurcates into a Decoupled Branch and two Coupled Branches, the latter exhibiting mass gap generation; (ii) dynamical dyonic flux tubes obtained from a time-dependent helical template, where the Gauss law ideal bifurcates the system into Coulomb, Dyonic, and symmetric Meissner branches. In the Meissner branch, an Artinian asymptotic truncation yields Bessel-type exponential screening, stabilized by a temporal dominance condition; and (iii) dynamical $SU(3)$ configurations where the Gauss law ideal bifurcates the solution space into four distinct phases. The non-trivial branches enforce a kinetic cancellation mechanism that maps the amplitude dynamics onto a generalized $x^2y^2$ chaotic oscillator. Across these settings, the framework provides a methodical approach to characterize the classical solution space of strongly coupled gauge theories.

Intrinsically protected superconducting qubits are a promising route toward enhancing coherence times and advancing hardware towards applications in quantum computing. The $\cos(2\varphi)$ qubit achieves protection against qubit relaxation by allowing only the coherent tunneling of pairs of Cooper pairs, resulting in Cooper-pair parity symmetry and thereby suppressing charge-induced errors. In this work, we experimentally realize a $\cos(2\varphi)$ qubit by Fourier engineering the energy-phase relation in a multi-junction superconducting circuit. Using an interference-based architecture, we are able to suppress the odd harmonics of an effective qubit potential and we observe good agreement between the measured transition spectrum and the effective theoretical model. We further investigate the energy relaxation time as a function of external flux and find that the qubit lifetime at the flux symmetry point is limited by $1/f$ flux noise. This strong sensitivity arises from residual fluctuations in the first harmonic, which possesses a large prefactor despite being nominally canceled. In contrast, a fluxonium qubit with a similar energy spectrum and noise amplitude is less affected by flux noise, highlighting a key challenge for interference-based protection schemes.

Gravitational waves (GWs) from distant sources such as inspiralling and merging stellar-mass compact binaries, intermediate-mass and supermassive-binary-black-hole can be gravitationally lensed by intervening objects, ranging from stars and primordial black holes to galaxies and clusters. Depending on the GW wavelength relative to the lens scale, lensing occurs in two regimes: geometric optics, producing multiple images with time delays and magnifications, and wave optics, resulting in frequency-dependent waveform modulations. Lensed signals are identified via parameter overlap between event pairs or characteristic frequency-dependent modulations that distinguish them from unlensed signals. Detection rates depend on the redshift and mass distributions of sources and lenses, with promising prospects for future observatories. Once confirmed, lensed GWs will be powerful probes of fundamental physics and cosmology: they can constrain dark matter, lensing structures, the Hubble constant, and other cosmological parameters. In this review, we provide a concise overview of GW lensing, covering the theoretical framework, predicted detection rates, search strategies, and applications. We conclude with prospects and future directions for observing and exploiting lensed astrophysical GW events.

We demonstrate in situ removal of a transport-blocking defect on a surface-electrode ion trap device using a Q-switched Nd:YAG 532 nm pulsed ablation laser. This approach eliminates the need to vent and rebake the vacuum system, providing a low-overhead defect-remediation technique well suited for ion-shuttling architectures where system modifications typically incur substantial downtime - particularly in shuttling focussed experiments operating at temperatures that necessitate bakes. Additionally, the hardware used is readily available in many ion trap laboratories, making this solution attractive to experiments operating in such regimes. Following ablation, we observe near-unit shuttling success rates across the previously obstructed region and measure micromotion levels that remain within acceptable limits. This technique enables rapid, reliable restoration of transport pathways without interruption to experimental operation.

The cavity-mediated coupling between magnons in an yttrium-iron-garnet (YIG) sphere and a superconducting qubit has recently been demonstrated as a new platform for preparing macroscopic quantum states. Here, based on this system, we propose to entangle two magnon modes in two YIG spheres by driving the qubit with a two-tone field and by appropriately choosing the frequencies and strengths of the two driving fields. We show that strong entanglement can be achieved with fully feasible parameters. We further provide a detection scheme for experimentally verifying the entanglement. Our results indicate that macroscopic entanglement between two magnon modes in two millimeter-sized YIG spheres, involving more than $10^{18}$ spins, can be realized using currently available parameters, which finds promising applications in fundamental studies, such as macroscopic quantum mechanics and the test of unconventional decoherence theories.

We develop a comprehensive theoretical framework that unifies quantum emission dynamics in one-dimensional Lieb lattices, bridging the gap between ideal flat-band coherence and realistic narrow-band dissipation. By coupling an emitter to sublattices with finite flat-band wavefunction overlap, we activate a collective, size-independent interaction fundamentally distinct from dispersive-band processes. Controllably breaking lattice symmetry transforms the flat band into a narrow dispersive band, enabling a continuous crossover from non-Markovian to Markovian dynamics governed by the competition between coupling strength and engineered bandwidth. Crucially, we derive explicit scaling laws that provide a quantitative blueprint for tuning spontaneous emission from coherent trapping to Markovian decay. Our work provides a unified framework that connects idealized flat-band physics to emerging narrow-band platforms such as moir$\rm\acute{e}$ photonic crystals, offering a practical toolkit for interpreting experiments and engineering quantum emission in structured photonic environments.

We generalize the unfolding of a Reed Muller distillation factory of Ruiz et. al. by exhibiting the algebraic structure that the unfolding is based on. We describe a 2D local layout for the Z stabilizers of a distance 4 Reed Muller distillation factory and a 3D local layout for the Z stabilizer of a distance 4 and a distance 7 Reed Muller distillation factory. Given input T states with infidelities $p=10^{-3}$, the 2D local distillation factory with distance 4 outputs a CCZ state with infidelity $p=8.256 \times 10^{-9}$ and the 3D local distillation factory with distance 7 outputs a T state with infidelity $p=1.1811 \times 10^{-17}$.

Quantum metrology promises precision beyond classical limits, yet environmental noise typically degrades the quantum resources required for such enhancement. In this work, we investigate frequency estimation in noisy continuous-variable systems, focusing on two complementary strategies to mitigate decoherence: Hamiltonian engineering and the exploitation of non-Markovian dynamics. By embedding squeezing directly into the system Hamiltonian, we show that the quantum Fisher information (QFI) may acquire a tunable higher-order time dependence, leading to enhanced sensitivity in the short-time regime. Moving beyond the Markovian approximation, we employ the quantum Brownian motion model to demonstrate that structured environments with finite memory can induce information backflow, temporarily restoring and even improving estimation precision relative to the unitary limit. We further assess the achievability of these bounds via Gaussian measurements, identifying regimes where homodyne, heterodyne, and optimized general-dyne measurements saturate the QFI, and noting that stronger squeezing widens the gap, potentially requiring non-Gaussian measurement strategies. Our results establish that jointly tailoring system Hamiltonian and environmental memory offers a viable route toward robust quantum-enhanced frequency estimation in open systems.

We consider the kinematic axioms of quantum mechanics projectively. Instead of normalized (pure) states up to global phase, states become one-dimensional subspaces of vector spaces. This process of projectivization is functorial and lax monoidal. For qubits it identifies the Bloch sphere with the Riemann sphere. We interpret a fragment of the ZXW-calculus projectively and thereby provide an alternate derivation of the arithmetic GHZ/W-calculus of Coecke et al. We find meromorphic functions that characterize the coherent behaviour of circuits for logical state preparation of quantum codes and magic state distillation.

Differential phase shift keying (DPSK) constitutes a pathway towards practical quantum key distribution by using affordable commercial technologies, and robust theoretical foundations. Recent advances in the security of DPSK have proven its security against general adversaries, albeit requiring limitations, including strong repetition rate constraints at the security proof and costly statistical estimators. In this work, we overcome said limitations by leveraging recent techniques in variable-length general security by using entropy accumulation techniques based on Rényi leftover hashing, together with conic optimization methods. Our approach achieves secret key rates with $10^5$ signals beyond 12 dB, constituting a robust proof of the experimental implementability of industrial-grade DPSK.

The massive Majorana field in $1+1$ dimension is employed to investigate the violation of the Bell-CHSH inequality in relativistic Quantum Field Theory. We give an explicit rapidity-space realization of the Summers-Werner modular-localization construction and reduce the vacuum Bell-CHSH correlator to a single spectral weight $h^2(ω)$ for the modular operator. The resulting analytic families approach the Tsirelson bound in the vacuum state as their spectral weight concentrates near $ω\approx0$, corresponding to the eigenvalue $λ^2 \approx 1$ of the modular operator.

Analog quantum simulators emulate complex many-body dynamics through native continuous-time evolution under hardware-defined interactions. Yet once a platform is specified, its interaction structure is largely fixed by the underlying hardware, restricting the Hamiltonians that can be realized and limiting programmability. Here we introduce universal analog quantum simulation (UAQS), a hybrid framework that systematically expands the range of accessible quantum evolutions within a given analog platform. UAQS employs optimized continuous-time control fields to engineer target dynamics directly, avoiding decomposition into discrete gate sequences. By preserving native analog evolution while extending the set of achievable Hamiltonians, UAQS transforms fixed-interaction analog devices into programmable simulators. Numerical studies on representative architectures, including superconducting circuits and Rydberg-atom arrays, show that UAQS accurately reproduces non-trivial many-body dynamics beyond the intrinsic interaction structure of the hardware. These results establish UAQS as a practical route toward programmable analog quantum simulation.

Hexagonal optical lattices, emulating graphene and hexagonal boron nitride (h-BN) structures, provide a versatile platform for exploring strongly correlated quantum matter. Using continuous-space exact diagonalization and quantum Monte Carlo simulations, we investigate the phase diagrams of ultracold bosons in honeycomb and h-BN lattices. For the honeycomb lattice, we find significant deviations from the standard Bose-Hubbard model even for strong lattice amplitudes. We observe suppressed Mott insulator lobes and the absence of higher-order insulating phases, attributed to strong density-assisted tunneling effects. In the h-BN case, a rich phase diagram emerges, featuring multiple Mott lobes with various sublattice occupations, driven by the interplay of lattice asymmetry, interactions, and particle filling. Our results highlight the necessity of continuous-space treatments for capturing the full complexity of bosonic quantum phases in hexagonal geometries, paving the way for experimental realizations with ultracold atoms and further theoretical work.

We propose a variational method for constructing the eigenvalues and generalized eigenvalues for an arbitrary $N\times N$ complex matrix. The quantum part of our algorithm is based on encoding the matrix elements into the pure state of a quantum system and expressing the loss function with optimization parameters in terms of certain probability amplitudes in the superposition state. The principal step of this algorithm is the measurement of the ancilla state that removes all extra terms from the above superposition and allows to probabilistically construct the required loss function along with its derivatives with respect to the optimization parameters. These output data are used to find the new values of optimization parameters for the next iteration of the loss function in the gradient optimization method. The depth and size of the circuit for this algorithm are, respectively, $O(N^2 \log N)$ and $O(\log N)$.

The LCDM model has been presented with a number of cosmic tensions in the face of precision cosmological data, suggesting the presence of a dynamical dark energy component. In this context, we investigate the cosmology arising from a generalisation of Brans-Dicke theory, with a non-minimally coupled scalar field characterising deviations from standard general relativity, and having a non-canonical kinetic term. By reformulating the field equations into an autonomous set of dynamical equations, we use the methods of dynamical systems to investigate the equilibrium states of the system and their stability for a set of widely-used potentials, namely the constant, power-law, and exponential potentials, with the flow visualized using bounded phase portraits. Furthermore, we investigate the physical meaning of the critical points, and we find viable solutions that can reproduce the characteristics of the $Λ$CDM model at background level for each of the three potentials. Furthermore, in each case, we observe that the dynamical behaviour differs noticeably from that observed in other scalar-tensor models due to the non-minimal coupling and non-canonical field, despite using similarly defined dynamical variables.

Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably approximating deep circuits representing potential landscapes becomes crucial for simulating real quantum systems. Variationally approximating unitaries allows for shallower circuits and accuracy tunable to hardware fidelity, so long as the observable quantities are preserved. We show the variational compression of Trotter terms preserve reaction rate coefficients via classical emulation of a hybrid quantum-classical optimization method, as well as fast-forwarded adiabatic dynamics on quantum hardware. Compressed circuits can be incorporated with product-formula-based time evolution to approximate dynamics of a particle in two coupled harmonic potentials, allowing tunability when removing high-cost qubit interactions. Approximate rate coefficients are recovered after substituting terms in a nonadiabatic dynamic process, giving proof-of-principle for observable preservation under variational optimization. Attention is paid to minimizing qubit and gate-count resources.

Quantum error correction (QEC) enables fault-tolerant quantum computation but requires operating quantum hardware at physical error rates below code-dependent thresholds, which remains challenging for current devices. We introduce syndrome resampling, a general method that increases QEC thresholds of any decoder and suppresses logical errors without additional hardware, decoding modifications, or code-specific assumptions beyond syndrome statistics. The method exploits the fact that syndromes with low probability are likely to lead to logical failure, therefore biasing syndrome averages towards most likely syndromes effectively increases logical fidelities. We establish a direct connection between the Rényi coherent information (RCI) and powers of the syndrome probability distribution, showing that resampling syndromes according to these powers combined with maximum likelihood decoding (MLD) realizes a family of optimal thresholds associated with phase transitions in the RCI. Numerical simulations of surface codes demonstrate that syndrome resampling substantially increases thresholds for both optimal and suboptimal decoders and reduces logical error rates by up to four orders of magnitude in experimentally relevant regimes. We further show that syndrome resampling can be effectively implemented from finite data and combined with decoding-based post-selection to achieve additional gains. Finally, applying the method to existing experimental QEC data yields up to two orders of magnitude reduction in logical error rates without requiring additional measurements. Our results provide a practical and decoder-agnostic route to improved logical fidelities in near-term QEC experiments.

We investigate the problem of classical big bang singularity in a plane-symmetric Bianchi type-I universe within the Wheeler-DeWitt (WDW) framework of quantum gravity. To address the problem of time, we employ the Page-Wootters formalism, which provides a relational notion of dynamics by conditioning the global state on a clock subsystem. Using Misner variables, the WDW equation assumes a Klein-Gordon (KG) type form. Its general solution is constructed as a Gaussian superposition of momentum eigenstates, resulting in an entangled global state between the clock and the remaining subsystem. Within this relational framework, we construct conditional states and obtain the corresponding probability density consistent with the KG-type inner product. The resulting conditional probability density vanishes in the limit of zero volume for all clock values, indicating quantum resolution of the classical singularity. We further show that positivity of the probability density imposes constraints on the admissible clock values, which depend on the parameters of the Gaussian wavepacket. These results highlight the essential role of quantum correlations in the emergence of relational dynamics, and demonstrate that the Page-Wootters formalism provides a consistent and nonsingular probabilistic description of quantum cosmology.

We systematically investigate the entanglement dynamics of quasiperiodic systems across their extended, critical, and localized phases, aiming to identify dynamical signatures that can clearly distinguish the critical phase from the other two. Focusing on the extended Harper model, we complement the half-chain entanglement entropy with the spatially resolved subsystem information capacity (SIC) and demonstrate that the critical phase exhibits a pronounced spatial heterogeneity that is absent in the extended and localized phases. In the steady state, the SIC reveals a stepwise ramp as a function of subsystem size, reflecting an underlying fragmentation of the chain into weakly connected subregions. Dynamically, information initially localized within such a subregion can undergo coherent long-lived oscillations, dubbed subregion echoes, whose period scales with the subregion length, in quantitative agreement with a quasiparticle picture of confined quasiparticle reflections. We trace this internal fragmentation to the incommensurately distributed zeros (IDZs) in the off-diagonal hopping terms of the Hamiltonian. To establish the generality of the SIC as a diagnostic tool, we further apply it to a mobility-edge phase with coexisting extended and localized states and to a critical phase that does not originate from IDZ fragmentation, and show that the SIC can cleanly distinguish these scenarios through their distinct steady-state profiles, initial-site sensitivities and the presence of subregion echoes. Our results establish the SIC as a powerful real-space probe for diagnosing critical phases and for uncovering the bottlenecked connectivity that underlies their multifractal structure.

Whether chirality-induced spin selectivity (CISS) reflects coherent SU(2) spin rotation or incoherent spin-dependent filtering is a central unresolved question in molecular spintronics, with implications ranging from asymmetric chemistry to quantum information. We show that these two scenarios are distinguishable by a sharp symmetry criterion on the superexchange interaction mediated by a chiral molecular bridge. Coherent CISS, implemented as a unitary spin rotation of the tunneling electron, generates a giant Dzyaloshinskii-Moriya (DM) interaction with ratio |D|/JH up to 3, which is two orders of magnitude beyond intrinsic Rashba spin-orbit coupling in Si/SiGe. Incoherent CISS, represented by any Hermitian (non-unitary but spin-diagonal) tunneling matrix, produces D = 0 identically; we prove this as a structural theorem, reinforced by a Lindblad argument that dissipative spin filtering cannot modify virtual-tunneling-mediated superexchange. The DM interaction thus serves as a coherence order parameter, nonzero only when quantum amplitudes for opposite-spin transmission maintain a fixed relative phase. We derive closed-form angular, enantiomeric, and sensitivity signatures and show that the critical coherent rotation angle lies two orders of magnitude below current transport-inferred values and is accessible to existing 10 kHz exchange spectroscopy in gate-defined quantum dots. Five candidate molecules are predicted to exceed this threshold by one to two orders of magnitude even in a conservative interface-amplification scenario. The proposed measurement converts a long-standing transport controversy into a binary spin-qubit experiment with quantum-amplitude resolution.

Far-field optical imaging inevitably involves low-pass spatial filtering, limiting the resolution. Moreover, conventional imaging suppresses high spatial frequency components close to the cutoff, making them invisible under noise, particularly the shot noise arising from discrete and random nature of quantum light. Here we propose and implement a method for reducing the effect of this noise by optically pre-processing the incoming light prior to detection, thereby optimizing the quantum measurement performed on it. Our scheme, termed Fourier Domain Division (FDD), partitions the Fourier plane into multiple regions for independent detection and subsequent post-processing for image reconstruction. By analyzing the quantum and classical Fisher information, we show that our method is advantageous with respect to direct imaging for high spatial-frequency components. As a result, the number of photons required to achieve a certain signal-to-noise-ratio in the Fourier domain is reduced, thus enhancing the overall resolution in the photon-starved regime. We demonstrate our method in microscopy, achieving 5-fold improvement of Fisher information on high spatial-frequency components. Unlike active super-resolution methods, FDD is passive, making it broadly applicable in microscopy and other imaging scenarios where active illumination is impractical, including astronomy and remote sensing. Our work establishes a general strategy for designing quantum optimized superresolution imaging systems, bridging fundamental quantum limits, practical image analysis and computer vision applications.

Variational quantum circuits with angle encoding implement truncated Fourier series, and architectures arranging $N$ qubits with $L$ encoding layers each -- sharing encoding budget $E = NL$ -- generate identical frequency spectra, identical frequency redundancy, and require the same minimum parameter count for coefficient control. Despite this equivalence, trainability varies substantially with architecture shape $(N,L)$ at fixed $E$. We identify structural rank deficiency of the coefficient matching Jacobian $J$ as the mechanism responsible. For serial single-qubit architectures, we prove $\mathrm{rank}(J) \leq 2L+1$ regardless of parameter count $P$, with $\dim(\ker J) \geq P-(2L+1)$ growing without bound -- a phenomenon we term \emph{structural gradient starvation}: a growing fraction of parameters become structurally decoupled from the loss as $P$ increases at fixed $L$. Parallel architectures avoid this via independent phase trajectories, ensuring $σ_{\min}(J^{(\mathrm{par})}) > 0$ generically for $P \leq 2E+1$, so no parameter lies in $\ker J$. For practitioners, we further show that the two natural routes to increasing parameter count have fundamentally different effects: adding feature map (FM) layers monotonically strengthens the Jacobian QFIM eigenvalue spectrum and achieves $R^2 \geq 0.95$ with $1.6$--$2.2\times$ fewer parameters than adding trainable blocks across all tested architectures, while trainable blocks improve training only through the classical interpolation mechanism with no quantum-specific benefit.

We investigate light-cone smearing induced by quantum fluctuations of gravitons and its implications for the ultraviolet structure of quantum field theory. By treating the first-order correction to Synge's world function as an operator, we show that the retarded Green's function is smeared by the variance of graviton fluctuations. The smearing width depends on the quantum state of gravitons: vacuum fluctuations generate a Gaussian smearing of the light cone, coherent states shift the light-cone position, and squeezed states modify the smearing width itself. We then apply the smeared Feynman propagator to one-loop self-energies in interacting scalar field theories. In both the $φ^3$ bubble diagram and the $φ^4$ tadpole diagram, the short-distance singularities responsible for the usual ultraviolet divergences are regularized by a nonzero smearing width. We also estimate the contribution from primordial gravitons generated during inflation and show that it induces a finite correction of order $10^{-10}$ to the one-loop self-energy. Our results suggest that the quantum state of gravitons can leave a finite imprint on the causal and short-distance structure of quantum field theory.

Large language models (LLMs) have transformed artificial intelligence, yet classical architectures impose a fundamental constraint: every trainable parameter demands classical memory that scales unfavourably with model size. Quantum computing offers a qualitatively different pathway, but practical demonstrations on real hardware have remained elusive for models of practical relevance. Here we show that Cayley-parameterised unitary adapters -- quantum circuit blocks inserted into the frozen projection layers of pre-trained LLMs and executed on a 156-qubit IBM Quantum System Two superconducting processor -- improve the perplexity of Llama 3.1 8B, an 8-billion-parameter model in widespread use, by 1.4% with only 6,000 additional parameters and end-to-end inference validated on real Quantum Processing Unit (QPU). A systematic study on SmolLM2 (135M parameters), chosen for its tractability, reveals monotonically improving perplexity with unitary block dimension, 83% recovery of compression-induced degradation, and correct answers to questions that both classical baselines fail -- with a sharp noise-expressivity phase transition identifying the concrete path to quantum utility at larger qubit scales.

We explore and discuss corrections to the Newton potential from the quantum effects of conformal matter fields. In this special case, one can compare different approaches, including that of effective quantum gravity and another, based on the conformal (trace) anomaly. The comparison of these two methods is the main focus in the present work. Using the anomaly-induced effective action of gravity requires fixing the quantum vacuum state, similar to what is done in the description of black hole evaporation. In the Boulware vacuum state, we compute the anomaly-induced stress tensor and the first-order correction to the classical gravitational law. The quantum correction to the Newton's potential derived in this way, differs from the result calculated in a way analogous to the effective approach to quantum gravity. The only way to reconcile the two approaches for deriving the leading semiclassical corrections to Newtonian potential is to modify the asymptotic behavior of the average of the energy-momentum tensor in the Boulware vacuum state, as has been recently discussed in the literature.

We present a fault-tolerant mapping of rotated surface codes onto a $2\times N$ silicon spin-qubit railway architecture, utilizing electron shuttling to resolve the wiring fan-out bottleneck. Employing circuit-level noise modeling, we evaluate threshold performances across various noise biases. We demonstrate that shuttling check qubits instead of data qubits fundamentally improves system thresholds. Crucially, under a noise model biased towards dephasing for spin-qubit shuttling, the non-CSS XZZX surface code outperforms standard CSS variants. By tailoring the topological code to this specific inherent bias, we show that the Megaquop footprint is achievable with a distance 7 code requiring a $p = 10^{-3}$ physical error rate, highlighting a pathway for substantial hardware reductions in early fault-tolerant quantum processors.

Gauge theories form the foundation of the Standard Model of particle physics. These theories can exhibit confinement, where charged particles only occur in bound states, connected by flux strings whose energy grows linearly with separation. Simulating the real-time dynamics of such strings, including their breaking, remains a major challenge for classical computations and a promising target for quantum simulations. While recent quantum simulation experiments explored string-breaking dynamics in abelian lattice gauge theories, non-abelian theories are qualitatively distinct because gauge fields themselves carry charge. Here, we report the first quantum simulation of genuine non-abelian string-breaking dynamics in a pure SU($2$) lattice gauge theory, where gauge-field self-interactions drive string breaking even in the absence of dynamical matter. Our results are obtained on a trapped-ion quantum computer, using native qudit Hilbert spaces to encode truncated gauge fields on a ladder geometry and implement digital Trotter dynamics. We experimentally study unbreakable and breakable strings generated by fundamental and adjoint static charges, respectively. We locally resolve string oscillations and coherent string breaking through the creation of gluonic excitations driven by non-abelian plaquette interactions. Our work establishes hardware-efficient, problem-tailored qudit simulations as a promising route for accessing non-perturbative dynamics relevant to high-energy physics.

Recent demonstrations of squeezing generation using Traveling Wave Parametric Amplifiers (TWPAs) have opened the way for the application of broadband microwave squeezing in quantum sensing, quantum-enhanced detection, and continuous-variable quantum information. Here we demonstrate vacuum squeezing generation via residual three-wave mixing (3WM) in a Josephson TWPA based on superconducting nonlinear asymmetric inductive elements (SNAILs) with alternated magnetic flux polarity. By investigating competition between four-wave mixing (4WM) and 3WM nonlinearities, we prove that vacuum squeezing generation via residual 3WM is possible when a careful choice of the operating flux point is adopted. Our study provides valuable insights on the impact of competing nonlinearities on TWPA squeezers, potentially extending the range of applications in the framework of microwave photonics.

The quantum Pontus-Mpemba effect is a counterintuitive phenomenon in which a quantum system relaxes faster through a two-step evolution protocol than through a single, unquenched relaxation. This work proposes its realization in cavity quantum electrodynamics using the Jaynes-Cummings model with photon loss. The model captures the coherent interaction between a two-level atom and a single quantized mode of a lossy cavity, providing a minimal yet realistic setting to explore dissipative quantum dynamics. Restricting the analysis to the single-excitation sector, the dynamics feature damped vacuum Rabi oscillations for weak dissipation that transition to near-exponential atomic decay under strong dissipation. A sudden quench of the cavity decay rate generates distinct relaxation trajectories from the same initial atom-cavity state. The atomic excitation then displays a non-monotonic, accelerated decay, where a trajectory with a quenched dissipation relaxes faster than fixed-loss evolution. The effect originates from the interplay between coherent atom-photon exchange and cavity dissipation, establishing a clear and experimentally accessible realization of the quantum Pontus-Mpemba effect in both optical and circuit QED platforms.

The aim of this paper is to present a general way to calculate quasi-normal modes (QNM) of the Teukolsky equation for higher dimensional (d > 4) Kerr spacetime with compactified extra dimensions. In order to do so, we develop a formalism derived from spinors: we call it multispinor formalism. It is based on vectors of two-spinors and permits us to develop a formalism analogous to that of Newman-Penrose in 4d. From this we show how to derive the Teukolsky equation for gravitational perturbations and calculate the QNM. In order to keep calculations simple we fix, as an example, the dimension number to be six, but the work can be readily generalized to other spacetime dimensions.

Scaling symmetries have previously been examined for classical field theories described by singular Lagrangians; in this article, we apply these results to the first-order formulation of General Relativity. It is shown that the dynamical content of the Hilbert action may be formulated in terms of the conformal spacetime geometry, together with a dissipative sector, which is required in order to compensate the elimination of the notion of scale encoded by the conformal factor. Further, we consider the linearisation of the equations of motion of the scale-invariant action, demonstrating that the first-order metric perturbations satisfy a free wave equation, as expected. The second-order dynamics, describing gravitational backreaction, are found to be sourced by quadratic combinations of the first-order perturbations. However, these dynamics are non-conservative, as is made manifest by the presence of terms which couple the action sector with the geometrical degrees of freedom.

Spin-carrying single-photon emitters operating in the telecommunication C-band (1530-1565nm) are prime candidates for integrated spin-photon interfaces, offering seamless compatibility with existing fiber-optic infrastructure, an essential component for future quantum networks. In this context, erbium-dopants ($\text{Er}^{3+}$) are particularly compelling due to their exceptional emitter properties, including small spectral diffusion and long spin coherence times. However, their low C-band photon-emission rate and operation at cryogenic temperatures has limited the realization of this technology. In this work, we demonstrate fully integrated single-photon emission from an ion implanted $\text{Er}^{3+}$-embedded into a 4H-silicon-carbide-on-insulator (4H-SiCOI) microring resonator operating at room temperature. By optimizing the mode overlap between the resonator and the $\text{Er}^{3+}$-defect, we achieved a $\sim$70$\times$ Purcell enhancement and recorded small spectral diffusion of $\sim$54 MHz. We further characterize the $\text{Er}^{3+}$ single photon emission via photon correlation g$^{(2)}$-histograms and investigate its performance under varying magnetic-field, demonstrating Zeeman splitting on single emitters.

We develop a new theory of an optical force exerted on a carbon nanotube (CNT) with a nonlocal conductivity. The optical force is expressed in terms of the surface current density and the axial electric field on the CNT surface. To determine these quantities, we employ an integral-equation-based approach in terms of the current density. The analysis is constructed for a finite-length cylindrical CNT by rigorously accounting for edge effects. In addition to numerical solutions of the integral equation, we obtain an approximate analytical expression for the optical force acting on the CNT, which shows good agreement with numerical simulations. We also demonstrate the existence of some frequency ranges in which the optical force becomes negative, corresponding to the optical pulling effect. Such a pulling behavior is shown to originate from the nonlocality of the conductivity and to vanish in the local limit. This work advances theoretical understanding of optomechanical interactions in finite-length low-dimensional conductors and clarifies the role of spatial dispersion in the emergence of optical pulling forces.

A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space process is required only to reproduce the Born density after integrating over momentum, the requirement fixes only an integrated current; the local drift and diffusion remain underdetermined. If one instead requires all Weyl-ordered expectation values, the phase-space object is fixed to be the Wigner function. For non-quadratic potentials the Wigner--Moyal generator contains higher-order, signed momentum-transfer terms, so it is not the Fokker--Planck generator of a positive Brownian diffusion. The exact Wigner function must therefore be reconstructed, in a stochastic representation, as a weighted empirical measure \[ \FW(\z,t)=\E_{\Pp}[W_tδ(\z-\z_t)], \qquad \z=(q,p), \] rather than the unweighted density of sampled carrier trajectories. With classical Hamiltonian flow as the carrier, all nonclassical correction beyond classical transport sits in the Moyal residual and can be represented by signed weights or branching events. The same split defines a residual diagnostic that vanishes for quadratic Hamiltonians and measures what classical carrier transport misses in anharmonic dynamics. The formulation also gives a forward--reverse relation for signed Wigner path measures. The ratio of forward and reversed contributions separates into a positive magnitude factor and a sign factor. This sign records the parity of the Wigner interference contribution; it is not a thermodynamic entropy production.

Single-photon sources that are bright, pure, and interference-ready are essential for quantum communication and photonic quantum information processing, but many solid-state platforms still rely on bulky optical excitation, careful alignment, and post-selection to achieve useful linewidth, stability, and brightness. Scalable quantum photonics instead requires turnkey quantum-light engines that can be triggered on demand, stabilized against environmental noise, and efficiently interfaced with fibers or photonic circuits. This review surveys recent progress in electronic and photonic integration of single quantum emitters in two-dimensional materials, focusing on localized excitonic emitters in transition metal dichalcogenides and defect-based color centers in hexagonal boron nitride. On the electronic side, we discuss electrical injection, fast modulation, electrostatic stabilization, and Stark tunability as routes to suppress blinking, spectral wandering, and charge-noise-induced broadening. On the photonic side, we review waveguide and resonator platforms that funnel emission into well-defined optical modes and, in some cases, enhance radiative rates through the Purcell effect. We connect these integration strategies to key source metrics, including single-photon purity, brightness, spectral stability, and photon indistinguishability. We conclude that the next stage of progress will depend on co-designed electronic and photonic architectures that jointly optimize on-demand operation, stabilization, tunability, and packaging-compatible optical interfacing.

This paper reports a Ricci-Gauss-Bonnet (RGB) dark energy model within the framework of Hořava-Lifshitz cosmology and presents a scalar-field reconstruction of the effective dark energy sector. In a spatially flat FRW background with a power-law scale factor, we derive analytical expressions for cosmological parameters, scalar field kinetic term, and the reconstructed potential. The reconstructed EoS parameter exhibits smooth transition toward a cosmological-constant-like regime at late times for suitable choices of the model parameters. The classical stability of the model is analyzed through the squared sound speed, and stable regions of the parameter space are identified. Finally, the generalized second law of thermodynamics is investigated at the apparent horizon, and it is shown that the total entropy variation remains non-negative in this model. From these results it can be concluded that the model provides a theoretically consistent description of late-time acceleration, with physical viability maintained within a specific range of the model parameters.

We propose a mixed quantum-classical hydrodynamic framework to model short-time inertial effects in the non-adiabatic evolution of a quantum solute coupled to a classical polar solvent. Drawing upon the work of Burghardt and Bagchi [Chem. Phys. 329 (2006), 343], we employ the Hamiltonian approach to incorporate consistent backreaction and preserve quantum decoherence beyond standard Ehrenfest dynamics. The solvent is treated as an ideal polar fluid and the quantum solute state is correlated to both the position and molecular orientation coordinates of the liquid. This approach retains essential solute-solvent correlations while significantly reducing the computational complexity of previous approaches. We further incorporate dissipative terms to capture both inertial effects and polarization relaxation. After establishing the general setting for non-local dielectric continua, the Marcus local approximation is integrated into the model thereby extending traditional solvation theory to account for collective fluid sloshing on fast timescales.

We investigate the optical appearance of rotating black holes embedded in dark matter environments through a phenomenological ray-tracing framework. Instead of focusing on a single dark-matter-dressed geometry, we use a comparative setting in which a regular Einasto-type dark-matter-sourced black hole and a cored-NFW halo black hole are promoted to effective rotating backgrounds. This allows us to separate profile-dependent effects from generic Kerr-like rotational features. We construct observer-screen images by numerical backward ray tracing and analyse the shadow boundary, lensing bands, transfer maps, and synthetic intensity distributions produced by semi-analytic accretion prescriptions. Particular attention is paid to the possible degeneracy between spin and the dark matter parameters, and to whether higher-order lensed images can provide stronger signatures than the primary shadow size alone. For the representative parameters considered here, the Einasto-supported geometry remains close to Kerr, while the cored-NFW case produces a larger apparent image scale and more visible deviations in the lensed structure. The framework developed in this work is lightweight and extensible, and can be used as a first step toward future radiative-transfer and low-resolution accretion-flow studies of rotating dark-matter-dressed black holes.

We show that the Bell-state phase of a polarization-entangled photon pair controls the biexciton eigenstate distribution produced by entangled two-photon absorption (ETPA) in monolayer WSe$_2$. In a frequency-nondegenerate ladder scheme, two independent valley pathways ($K$ and $K'$) share no intermediate state, so the biphoton phase sets the relative amplitude between them. Within the valley-symmetric limit this phase factorizes from the material response, and the resulting selection rule partitions the excitation among biexciton eigenstates according to the Bell-state phase $\varphi$. The symmetric Bell state ($\varphi = 0$) selectively drives bright eigenstates, while the antisymmetric state ($\varphi = π$) drives the exchange-dark eigenstate. No classical polarization source reproduces this $\varphi$-dependent eigenstate distribution. Including valley dephasing and intervalley scattering at 4~K, the phase-scan visibility exceeds $0.97$ for broadband SPDC ($T_e \sim 100$~fs) with high source purity.

Parity (XOR) classification requires detecting discrete, high-order feature interactions that smooth classical kernels cannot efficiently capture. We study how quantum kernel advantage depends on parity complexity, the number of features entering the XOR rule, and find a clear threshold behavior. We pair a ZZ quantum feature map with binary {0, pi} encoding (features median thresholded before circuit input) to expose parity structure. A binary encoding ablation, RBF SVM trained on the identical {0, pi} features, separates encoding from circuit effects: at low complexity (n = 5 features), binary RBF achieves 83.4% +/- 1.7% and the quantum kernel 81.2% +/- 1.9%, showing encoding drives performance there. At high complexity (n = 11 features, 11 qubits, r = 3 ZZ repetitions), all classical methods collapse to near-random (approx. 50%), binary RBF reaches only 54.3% +/- 1.1%, and the quantum ZZ kernel achieves 66.3% +/- 3.2% (mean +/- std, 10 seeds), a +12.0 percentage-point margin over the binary ablation and approx. 7x higher kernel-target alignment (0.094 +/- 0.020 vs. 0.013 +/- 0.001). These results identify parity complexity as a concrete axis along which genuine quantum kernel advantage, not attributable to encoding alone, emerges.

We investigate trilinear structures as a natural extension of the Hirota bilinear formalism in integrable systems. While bilinear equations are associated with Grassmannian geometry and Plücker relations, trilinear equations suggest a higher algebraic structure involving three-slot couplings of tau functions. Focusing on the stationary axisymmetric Einstein equations, we show that when the Ernst potential is written in a tau-ratio form, the nonlinear equation decomposes into a cubic sector containing all second-derivative terms and a quartic gradient envelope. The cubic sector is identified with a YTSF-type trilinear kernel. We formulate a general trilinear kernel criterion and apply it to the Tomimatsu--Sato solutions. In particular, we demonstrate that the $δ=3$ solution possesses the same trilinear kernel structure as the $δ=2$ case, with a universal normalization up to a constant factor. These results suggest that the trilinear kernel represents a universal structure governing the highest-derivative sector of the Ernst system, providing a new perspective on integrability beyond the bilinear hierarchy.

Tunneling ionization in static or slowly varying electric fields is a cornerstone of strong-field physics and provides the entry point for semiclassical descriptions of above-threshold ionization and high-harmonic generation. In conventional quantum mechanics, the Perelomov--Popov--Terent'ev (PPT) theory and its Ammosov--Delone--Krainov (ADK) form yield an ionization rate whose defining feature is an exponential dependence governed by an under-barrier (imaginary-time) action. Here we develop an analytical ADK-like tunneling model within \emph{space-fractional} quantum mechanics, where the quadratic kinetic energy is replaced by the Riesz fractional Laplacian of order $1<α\le2$. Working in a static electric field in the length gauge, we derive a closed-form tunneling exponent for a triangular exit barrier. The fractional kinetic operator deforms the conventional $I_p^{3/2}$ scaling to $I_p^{1+1/α}$ and introduces a characteristic $\sin(π/α)$ factor encoding the complex-phase structure associated with nonlocal dispersion. We position this benchmark relative to prior tunneling studies in fractional quantum mechanics (primarily scattering through model barriers and fractal potentials) and provide a validation protocol for testing the exponent in time-dependent simulations of the fractional Schrödinger equation under a constant field. The result establishes a transparent reference for static-field ionization in nonlocal quantum dynamics and a baseline for strong-field approaches extensions.

Periodically driven quantum systems, known as Floquet systems, provide a versatile platform for engineering novel topological phases absent in static settings. However, dynamically characterizing these non-equilibrium topological invariants remains a challenge. Here, we develop a Floquet perturbation theory in the extended Hilbert space to analytically describe the center-of-mass (CoM) dynamics of a wave packet. When applied to the driven Su-Schrieffer-Heeger model, our theory reveals that the CoM exhibits multi-frequency Zitterbewegung oscillations, whose spectral composition and phase are directly tied to the system's Floquet band structure. Crucially, we find that band inversions at topological phase transitions imprint distinct signatures in the CoM dynamics, including the emergence of low-frequency modes and phase shifts of the oscillatory trajectory. These dynamical signatures offer a practical protocol for detecting Floquet topological invariants, which we demonstrate for both high-frequency and strongly driven regimes. Our work establishes CoM dynamics as a simple and experimentally accessible probe for exploring topological phase transitions in Floquet systems.

Understanding the emergence of macroscopic irreversible hydrodynamics from the reversible unitary dynamics of isolated quantum many-body systems remains a fundamental challenge. Conventional approaches often force spin density dynamics into purely diffusive models, obscuring the microscopic interplay of pressure, spin current, and local friction. Furthermore, reconciling true irreversibility with strictly unitary evolution raises profound questions about the role of the observer's temporal resolution. In this paper, we introduce a fully data-driven framework based on generalized Extended Dynamic Mode Decomposition (gEDMD) integrated with the Mori-Zwanzig projection. By expanding the observable dictionary to explicitly include spin currents, we directly extract the Navier-Stokes hydrodynamic coefficients from a chaotic XXZ spin chain across varying temporal coarse-graining scales. Our unconstrained extraction reveals a profound physical dichotomy: the mechanical elasticity ($c^2$) is intrinsically derived from the exact unitary dynamics, preserving strict microscopic reversibility. In stark contrast, the macroscopic friction ($γ$) and kinematic viscosity ($ν$) exhibit zero net dissipation, oscillating rapidly around zero in the exact-derivative limit. We demonstrate that genuine macroscopic transport cannot be established without finite temporal coarse-graining. By introducing a finite observation timescale ($Δt_{\rm cg} > 0$), the system passes through a distinct crossover timescale where these reversible fluctuations average out, establishing an intermediate functional regime that yields strictly positive friction and viscosity. Our results clearly demonstrate that macroscopic friction in isolated quantum systems is not an absolute property, but fundamentally an emergent phenomenon dictated by the temporal resolution of the observer.

Astrophysical formation channels of stellar-mass binary black holes (sBBHs) can induce significant orbital eccentricities in their early inspiral. We analyze the implications on the stochastic gravitational-wave background (SGWB) from unresolved sBBHs, which can be detected with the Laser Interferometer Space Antenna (LISA). We develop an improved SGWB model for the case of an idealized Dirac-delta eccentricity distribution, and extend it to the more astrophysical case of a thermal distribution. Using a fully Bayesian framework, we find that, if all binaries have a high initial eccentricity $e_0 \gtrsim 0.9$ at an orbital frequency of $f_{\rm orb} = 10^{-4}\,\mathrm{Hz}$, the resulting SGWB can be robustly distinguished from a background of quasi-circular sBBHs. For a thermal eccentricity distribution, the SGWB is consistent with a circular model when binaries form at $f_{\rm orb} = 10^{-5}\,\mathrm{Hz}$, but leads to significant systematic biases if formation occurs at $f_{\rm orb} = 10^{-4}\,\mathrm{Hz}$. We also show that, when eccentricity is properly accounted for, environmental effects such as dynamical friction can be distinguished from vacuum evolution, but only for sufficiently dense environments with gas densities $ρ\gtrsim 10^{-7}\,\mathrm{g\,cm^{-3}}$. Finally, we show that a LISA detection of the sBBH SGWB would place an upper bound on the maximum eccentricity of the sBBH population in the band of ground-based detectors, with direct implications for template modeling and data analysis. Our results highlight the importance of incorporating eccentricity in SGWB modeling to enable accurate astrophysical interpretation of LISA observations.

Efficiently learning expectation values of unknown quantum states via classical shadows has become an important primitive in both theoretical and experimental aspects of quantum computation. Typically, classical shadow protocols involve randomised measurements induced by sampling uniformly randomly from a compact group, a situation which is now quite well understood. In this work we go beyond this standard assumption, studying the classical shadow protocols occasioned by sampling uniformly randomly from the so-called compact symmetric spaces. We uncover a unifying theory of such protocols, extending the extent to which the general theory of classical shadows is understood at a mathematical level. Interestingly, for the estimation of observables sampled from certain distributions we further find that some of these protocols allow for slight improvements in sample-complexity over existing shadow schemes.

We develop a unified framework for testing gravity beyond General Relativity (GR) with continuous gravitational waves (CWs) from individual supermassive black hole binaries (SMBHBs). These long-lived, nearly monochromatic nanohertz signals offer unique strengths for precision tests of gravity, since their coherent phase evolution and inter-pulsar correlations in pulsar timing arrays (PTAs) retain detailed information about departures from GR over cosmological propagation distances. We consider three representative classes of deviations from GR: additional polarization states, modified dispersion relations, and parity-violating birefringence. For each, we derive the inter-pulsar cross correlation, the modified antenna response, and the propagation-induced pulsar-term phase delay. For non-tensorial polarizations, the CW cross correlation scales linearly in the alternative-polarization amplitude, compared to the quadratic scaling of the gravitational-wave background (GWB), provided the beyond-GR modes are sub-dominant. PTAs are also competitive for modified dispersion relations, where low frequencies enhance both the antenna-pattern modification and the pulsar-term phase delay. Birefringence, by contrast, is suppressed at nanohertz frequencies for most parity-violating theories. We validate the framework with injection-and-recovery simulations for breathing-mode and massive-graviton signals at current observational limits, recovering the injected beyond-GR parameters and distinguishing the CW signal from both correlated and uncorrelated background models. We further show that a pure-GR CW template recovers source parameters without significant bias when beyond-GR physics is present in the data, supporting a two-stage analysis strategy: identify candidates under GR, then test for deviations.

In this work, we present an exact static spherically symmetric vacuum solution of the New General Relativity (NGR) field equations. Unlike the Schwarzschild solution in General Relativity (GR), this solution is characterized by two parameters. Subsequently, using the four classical tests of relativistic gravity (perihelion precession, light bending, Shapiro time delay and gravitational redshift), a more stringent constraint on the value of the second parameter was derived compared to the original work [1].

We present a scalable quantum simulation framework for real-time dynamics of the multi-flavor Gross-Neveu model in 1+1 dimensions. Using superconducting quantum processors at utility scale, we develop a hardware-efficient Trotterization whose per-step circuit depth scales with fermion flavor number rather than total system size, enabling simulations beyond 100 qubits. A central contribution of this work is the Localized Diagonal Operator Approximation (LDOA), which systematically reduces the overhead associated with quartic interactions. We formulate diagonal unitary synthesis as a structured least-squares problem in phase space and obtain analytic solutions via the Moore-Penrose pseudoinverse. This formulation provides a principled and quantitatively controlled approximation: in the small Trotter-step regime, the unitary error is directly linked to the phase reconstruction error and vanishes asymptotically as the Trotter step size decreases. This establishes a clear mathematical foundation for the LDOA while significantly reducing two-qubit gate counts and circuit depth, and is broadly applicable to diagonal quantum operators with long-range structure, making it particularly well suited for quantum hardware with limited qubit connectivity. Using these techniques, we run large-scale simulations on IBM superconducting processors and study real-time observables, including density-density correlators. We benchmark against exact diagonalization and tensor network-based methods, finding strong agreement across system sizes. These results show that combining hardware-aware circuit design with rigorous approximations enables practical near-term simulation of interacting fermionic field theories and provides a scalable pathway toward more complex quantum field theory simulations.

It is shown that a standard one-dimensional coined discrete-time quantum walk can generate operationally admissible post-quantum correlations in a coin-position Bell scenario, without any modification of its unitary nearest-neighbor dynamics. Post-quantum features enter exclusively through an extended operational preparation of the coin, described by a complementarity-violating Hermitian trace-one operator, while physical consistency is enforced solely at the level of observable statistics via admissibility and no-signaling. The extended preparation admits an experimental emulation through a two-component quasiprobability reconstruction over physical coin states, at the price of an increased sampling overhead. The walk-generated coin-position entanglement can support CHSH values exceeding Tsirelson's bound, even though the walk dynamics remains fully standard. We also show that physically natural coarse-grained position measurements can render such post-quantum correlations operationally inaccessible, strongly suppressing observable Bell violations. The purpose here is to contrast the separation between the existence of post-quantum behavior and its accessibility under realistic measurement constraints.

We present the first direct computation of spatially averaged dynamical quantities in the local Universe, employing the Cosmicflows-4++ reconstruction and a covariant scalar averaging formalism. We extract the domain-averaged density, expansion rate, spatial curvature, and kinematical backreaction over cosmologically relevant domains around our Galaxy, extending up to a comoving radius of $300~\mathrm{Mpc}/h$. The resulting domain-averaged present-day energy budget features nontrivial variations with scale that reflect a nested structure within the cosmic neighborhood, including a large-scale void shell encompassing the local cosmic web. Remarkably, we find significant contributions to this energy budget from the average spatial curvature at the $\mathcal{O}(10\%)$ level on all probed scales. By contrast, the kinematical backreaction remains much smaller throughout the surveyed volume, reaching at most a $\mathcal{O}(1\%)$ contribution on the smallest scales considered, i.e., $30~\mathrm{Mpc}/h$. Convergence to the global $Λ$CDM background is not observed within this range of scales.

We show that in a minimal setup of two waveguide-coupled quantum emitters, separated by long distances and subject to an external field, time-delayed feedback can be a resource for sensing field gradients. While the field gradient induces a detuning between the emitters; the large interatomic separations render the system dynamics non-Markovian. We show that the quantum Fisher information (QFI) for estimating the detuning parameter, and thereby the field gradient, is enhanced in the presence of non-Markovian delay. Such an enhancement can be attributed to the formation of atom-photon quasi-bound states that enable the field to interact with the emitters for longer times, thereby gaining more information about their relative detunings. Additionally, in the presence of delay, the interaction between the emitters is mediated via multiple spectral modes of the field, further enhancing the sensing capabilities of the system. Our results establish non-Markovian time-delayed feedback and multimode reservoirs as a resource for distributed quantum sensing with waveguide-coupled quantum emitters.

Quadratic response tensors arise naturally in quantum kinetic descriptions, such as the quantum linear Boltzmann equation (QLBE), where they encode the coupled structure of drift and fluctuations beyond simple positive-definite forms. Motivated by this class of systems, we investigate how such response structures are modified under monitoring-induced coarse graining. Within the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) framework and under time-scale separation, Zeno elimination of fast degrees of freedom generates a subtractive renormalization with Schur-complement structure. As a result, positive definiteness of the response tensor is not preserved: coupling between slow and rapidly damped sectors can induce negative directions even when the microscopic tensor is strictly positive. We formulate a minimal effective flow capturing this mechanism and show that the competition between Schur-induced compression and anisotropic perturbations organizes the dynamics into distinct signature sectors. The resulting structure appears to be robust within the class of models considered and, in appropriate regimes, may be experimentally accessible. Our results establish a general framework for how quadratic response structures, as encountered in QLBE-type dynamics, are dynamically reorganized under Zeno-induced coarse graining.

Atom interferometry generates heterogeneous multivariate temporal streams governed by phase evolution, fringe dynamics, control variables, and auxiliary sensing measurements. Accurate forecasting of these signals is important for predictive monitoring, phase correction, and intelligent quantum sensing, but it requires effective modeling of long-range temporal dependencies and interactions among multiple sensing sources. This paper proposes BARFI-Q, a Quantum-Enhanced Block Attention Residual Fusion framework for multivariate time-series forecasting in atom interferometry. BARFI-Q integrates patch-based embedding, dual-branch temporal modeling, hierarchical fusion, adaptive block-attention residual aggregation, and a quantum feature-mapping module. Unlike conventional Transformer-based forecasting models with fixed additive residual paths, BARFI-Q adaptively reuses cross-depth information and enhances the fused latent representation through quantum feature mapping. To respect phase periodicity, the forecasting target is represented in circular space using sine and cosine components. Experiments show that BARFI-Q consistently outperforms strong baseline models across repeated runs and different historical window sizes. Fusion ablation results further confirm the benefit of jointly modeling channel-wise and spatial feature interactions. These results indicate that multiscale temporal learning, hierarchical fusion, adaptive residual routing, and quantum-enhanced latent transformation provide an effective framework for atom-interferometric time-series forecasting.

We study fluctuations of the metric in the postquantum theory of classical gravity, a covariant theory which couples a classical spacetime with quantum matter fields. Mathematical consistency requires spacetime to evolve stochastically. Starting from the classical-quantum path integral, we linearize around Minkowski space and perform a scalar-vector-tensor decomposition, identifying the stochastic modes: a classical spin-2 field and spin-0 scalar, both diffusing around their respective wave equations. There is also a non-dynamical vector and scalar field. These are related to the degrees of freedom found in quadratic gravity, but here interpreted as stochastic contributions to spacetime. We show that the action is positive semi-definite (PSD) on all dynamical modes, which is a necessary condition for the theory to consistently treat spacetime classically. We compute the two-point function and power spectral density corresponding to fluctuations of the Newtonian potential, and compare it to the excess noise found in LISA Pathfinder. This sets a bound on one combination of the two dimensionless coupling constants of the theory, while bounds on the stochastic gravitational wave energy density in a FLRW background constrain another combination. We derive the effective action for matter distributions, and find that bounds from decoherence experiments are constrained by fluctuations in the Newtonian potential $Φ$ and the curvature perturbation $ψ$. Finally, we show consistency between different formulations of the pure gravity theory, the Onsager-Machlup form of the action, the Martin-Siggia-Rose form, and that given by stochastic differential equations.

Quantum data-center networks must distribute entanglement between QPUs over paths whose length grows with system scale, but each entanglement-swapping step reduces the quality of the raw end-to-end state. Topology, multiplexing, and repeated connection attempts can increase the number of raw end-to-end copies available for a request, yet they do not answer the central resource question: whether those copies are sufficient to remove, via entanglement purification, the fidelity loss caused by multi-hop distribution. We study this question through a topology-independent black-box model of the network. Each elementary link is modeled as a Werner state with parameter $w_0$, so ideal swapping over an $\ell$-link path produces equal-quality raw copies with Werner parameter $w_0^\ell$; purification succeeds if it outputs at least one state with Werner parameter at least $w_0$ with probability at least $p_{\mathrm{th}}$. We compare recursive BBPSSW purification with higher-order $r$-to-$1$ bilocal-Clifford purification protocols of Jansen \emph{et al.}, using an all-in recursive schedule whose success probability is computed by exact dynamic programming. The resulting resource landscapes show a threshold structure governed by the Werner entanglement condition $w_0^\ell>1/3$ and demonstrate that multi-copy purification substantially improves both feasibility and copy efficiency. Across the evaluated grid, the Jansen family requires fewer copies than BBPSSW at more than $96\%$ of shared feasible points; at $p_{\mathrm{th}}=0.70$, the median copy budget drops from $268$ to $30$. These results provide a quantitative purification-resource benchmark for assessing whether future quantum data-center architectures can practically support hop-independent end-to-end entanglement quality.

Extreme mass-ratio inspirals (EMRIs), with their long-lived and highly relativistic orbital evolution, can probe strong-field spacetime geometry and provide an important means to test general relativity. In this work, we investigate EMRI waveforms in a Schwarzschild-like black hole spacetime arising in bumblebee gravity, where Lorentz symmetry breaking (LSB) is characterized by a dimensionless parameter $\ell$. We construct EMRI waveforms within the Augmented Analytic Kludge (AAK) framework using the modified orbital frequencies and fluxes. We find that $\ell$ significantly affects the orbital evolution and thereby modifies the waveform. These modifications grow with increasing $\ell$ and are further enhanced for more eccentric orbits. Furthermore, using Bayesian analysis, we obtain the posterior distributions of EMRI with the parameter $\ell$ included. Our results show that all injected source parameters are recovered within their $1\,σ$ credible intervals. We find that the bumblebee parameter $\ell$ can be constrained with an uncertainty of order $\mathcal{O}(10^{-4})$ by LISA.

We propose a simplified model for the cosmological constant in string theory flux vacua motivated by type IIB and F-theory compactifications. Relative to the Bousso-Polchinski model, small vacuum energy spacing occurs in thin wafers rather than thin shells. The model is applied to the entire Schöller-Skarke database of Calabi-Yau fourfolds, which exhibit $532,600,483$ distinct sets of Hodge numbers. The overwhelming majority of those ($99.95\%$ percent for some choices of parameters) exhibit a vacuum energy spacing of~$10^{-120}$ in Planck units or smaller. Brown-Teitelboim membrane nucleation transitions can populate this landscape of flux vacua. In the thin-wall approximation, and ignoring gravitational corrections, we find that the bubble transitions are always dominated by giant leaps in flux space. The age of the universe places a bound on Calabi-Yau topology that is satisfied for the entire Schöller-Skarke database.

We study electromagnetic perturbations and the associated quasinormal modes (QNMs) of parametrized static, spherically symmetric wormhole spacetimes, focusing on Damour-Solodukhin and braneworld geometries as well as their galactic extensions. Using the Bronnikov-Konoplya-Pappas parametrization, we express the metric functions in terms of a compactified radial coordinate and characterize the spacetime through far-field and near-throat parameters. The far-field coefficients govern the asymptotic structure and post-Newtonian behaviour, while the near-throat continued-fraction expansion captures the strong-field geometry near the throat. We first apply the parametrization to isolated wormholes and identify its range of validity, showing that non-polynomial metric functions can limit the convergence of the near-throat expansion and hence the accuracy of a truncated representation. We then extend the framework to a galactic Damour-Solodukhin wormhole embedded in a Hernquist dark matter halo. Imposing observational bounds from the shadow of Sgr A$^*$, we constrain the galactic compactness and deformation parameters and obtain an observationally viable parametrized metric. Within the allowed parameter space, we compute the fundamental QNM frequencies using the transfer matrix method and analyze the corresponding time-domain ringdown signals. We find that the damping rate is more sensitive to galactic compactness, whereas the oscillation frequency remains comparatively stable. Although the spectral shifts are small within the shadow-allowed region, the framework provides a systematic link between geometric parametrization, shadow constraints, and dynamical response. Our results establish an observationally consistent parametrized description of wormhole perturbations for strong-field tests of horizonless compact objects.

The execution cost of quantum algorithms is typically quantified through asymptotic gate counts and qubit register sizes, yet these metrics do not directly capture which genuinely quantum resources, and in what amount, must be created and maintained for the computation to succeed. The systematic quantification of such information-theoretic requirements in quantum computing protocols remains an extremely challenging open problem, despite their direct role in establishing quantum advantage. To address this gap, we investigate the generation of non-stabilizerness (or magic), one of the key resources, in the paradigmatic Shor's factoring algorithm, revealing a deep connection between intrinsic quantum complexity and the computational hardness of the underlying number-theoretic problem. By developing an explicit analytic theory, we demonstrate the fundamental role of magic in the successful execution of the algorithm, and show that Shor's routine maximally exploits the quantum resource in practically relevant regimes. Our findings create a concise conceptual link between the classical algorithmic difficulty of a task and the non-stabilizer price to solve it on quantum hardware, complementing standard circuit-cost analyses with a resource-based metric that is naturally aligned with the real bottlenecks of fault-tolerant quantum computing.

Ultrafast birefringence oscillations observed in superfluid helium provide evidence for anisotropic quantum squeezing of quasiparticle pairs. The measured response is a superposition of contributions from all vibrational modes, with dominant contributions from rotons, maxons, and Pitaevskii's plateau. The nonzero initial phase follows naturally from multimode interference.

We introduce kinetically constrained superradiance, a form of cooperative emission in which interactions imprint configuration-dependent energy shifts on optical transitions, splitting Dicke superradiance into multiple, frequency-resolved collective decay channels. Each channel selectively radiates from distinct many-body spin configurations, generating a hierarchy of dissipative time scales and sequential relaxation dynamics. Unlike conventional superradiance, where permutation symmetry enforces relaxation to a trivial steady state, configuration-selective emission can trap finite-momentum spin-wave excitations and stabilize long-lived entanglement. Remarkably, these correlations are generated purely by dissipation in the absence of entangling coherent dynamics. Our results point to modern superradiant experiments as scalable resources for dissipative engineering of correlated quantum states.

The quantum Fourier transform (QFT) is a fundamental primitive in quantum computation and quantum information. In this work, we generalize the QFT for finite groups to a QFT for finite-dimensional semisimple algebras, and give efficient quantum Fourier transforms for the partition algebra $P_n(d)$, Brauer algebra $B_n(d)$, and walled Brauer algebra $B_{r,s}(d)$. These algebras play important roles in generalized Schur-Weyl duality, statistical physics and many-body systems, and have recently found several applications in quantum algorithms. Unlike the group case, the Fourier transform over a semisimple algebra can be non-unitary. Nevertheless, we show that when the parameter $d$ is sufficiently large, the Fourier transform is well approximated by a unitary operator. Furthermore, we show that for each of the algebras $A$ from above, such an approximate Fourier transform can be implemented efficiently: we give a quantum algorithm with gate complexity $\mathrm{poly}(n,\log d,\log(1/\varepsilon))$ for approximating the Fourier transform to error $(d^{-1/2} + \varepsilon) \cdot \mathrm{poly}(|A|)$. Along the way, we establish several properties of the Fourier basis of semisimple algebras that may be of independent interest.

Some of the simplest wormhole solutions involve massless scalar fields that take imaginary values. Massless fields can be interpreted as coupling constants in asymptotically flat or asymptotically AdS gravity theories. We argue that wormhole effects imply an imaginary distance bound, an upper limit for the analytic continuation of the theory to imaginary values of these couplings. In string theory examples, we find explicit effects that render the low-energy theory invalid either before or precisely at this wormhole limit. We argue that the existence of such effects enforcing the distance bound is a general feature of string theories containing wormholes. In some cases, the bounds we discuss coincide with the weak gravity conjecture, and with the Kontsevich-Segal-Witten condition on complex metrics.

Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an instantaneous algebraic Hermitianization can be obtained locally from a positive metric operator, a stronger requirement is needed for dynamical equivalence: the similarity transformation must be proper, globally single-valued, and compatible with the modified quasi-Hermitian Schrodinger equation. We identify two distinct obstructions: geometric obstructions arising from the curvature of a metric-induced connection, and topological obstructions originating from non-trivial holonomies around non-contractible loops in parameter space. We derive explicit criteria for these obstructions and illustrate them with concrete examples. Our results establish a geometric and topological foundation for the Hermitianization of quasi-Hermitian systems, clarifying when they can be globally reduced to Hermitian ones and when intrinsic non-Hermitian features persist.

We prove a singularity theorem in semiclassical gravity without assuming global hyperbolicity or the null energy/curvature condition; the former is replaced by the weaker causality conditions of stable causality and past reflectivity, and the latter is replaced as is standard by the Generalized Second Law. This establishes in particular that the standard models of evaporating black holes are singular - i.e. they are null geodesically incomplete.

Recent results have established dramatic advantages in learning properties of quantum states when a quantum computer is available to process or jointly measure multiple copies of the unknown quantum state. Learning tasks can be accomplished with exponentially fewer copies of the state when compared to optimized classical learning strategies that are restricted to measuring one copy of the state at a time. While these results were established in abstract settings and for artificial learning tasks, they motivate the application of quantum computers to imaging and sensing of weak electromagnetic fields since these settings are ultimately concerned with the learning of unknown quantum states. In this work we apply these new results in quantum learning to the problem of learning Gaussian states of the electromagnetic field, which are germane since they describe most fields used in imaging and sensing. In order to connect with quantum learning theory, we consider the transduction of an $n$-mode Gaussian state into a register of qubits on a quantum computer followed by optimized measurements on these qubits to extract the parameters defining the original Gaussian state. We rigorously bound the number of copies of the Gaussian state required to achieve worst-case additive error in parameter estimates. The scaling of this bound with $n$ is exponentially better than naïve strategies for characterizing Gaussian states and matches recently derived bounds for characterization of Gaussian states using continuous-variable (CV) classical shadows. In addition, our bound has a polynomially better dependence on the energy of the multimode Gaussian state compared to the CV shadows protocol.

Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial basis for block-encoding any polynomial of a unitary. We characterize the achievable polynomial bases in terms of their orthogonality or biorthogonality with respect to a linear functional admitting an integral representation. Explicit expressions for the quantum signal processing angles are derived for families of polynomial sequences, including Hermite, Jacobi, and Rogers-Szegő polynomials. We show that $2n+2$ rotation angles are required to encode a sequence of polynomials in these classes up to degree $n$. We use this result to show that an $ε$-approximation of a smooth function $f$ can be block-encoded using $O(\log(1/ε))$ gates via its Hermite series expansion. The connections established with the theory of orthogonal and biorthogonal polynomials lead to a new method for solving the quantum signal processing angle-finding problem, yielding explicit expressions for the angles. They also provide a complete characterization of the polynomials achievable by $\mathrm{SU}(1,1)$-QSP in terms of their roots. Biorthogonality properties are shown to hold in the bivariate QSP setting, yielding a set of necessary conditions for achievable polynomials.

The no-boundary wavefunction for slow-roll inflation on the 3-sphere exponentially favors a small universe, in sharp disagreement with observations. We show that this problem is resolved by changing the spatial topology to the 3-torus. The sum over the ${\rm SL}(3,\mathbb{Z})$ family of geometries, computed using the theory of automorphic forms for ${\rm GL}(3)$, produces a wavefunction favoring a large inflating universe with ${\cal N} \gtrsim 250$ $e$-folds. We also compute corrections to the CMB power spectrum induced by torus moduli fluctuations.

We estimate the cost of simulating the two-dimensional Fermi-Hubbard model on a biplanar spin-optical quantum computing (SPOQC) architecture. Qubits are encoded in the honeycomb Floquet code, and we use a circuit-level noise model with explicit timings for each native physical operation. We benchmark lattice surgery and magic state preparation within each plane, and transversal CNOT gates between corresponding logical qubits across planes. We compile a plaquette-based Trotterization of the time evolution operator, mapping the two spin sectors of the Fermi-Hubbard model onto two physical planes. This architectural co-design eliminates fermionic swap operations and reduces the depth of each Trotter step to $4t_{\mathrm{synth}} + 90$ logical timesteps, where $t_\mathrm{synth}$ is the logical timestep cost of arbitrary-angle rotations, compared to $6t_\mathrm{synth} + 354$ in prior single-plane compilations. All error sources - algorithmic (Trotter), logical noise, magic state infidelity, and rotation synthesis - are treated jointly within a single 1% diamond norm budget. For an $L\times L$ lattice with hopping amplitude $t$ and on-site interaction strength $U$, setting $L=8$ and $U/t=8$, we estimate a total runtime of approximately $2$ hours using $1.35\times 10^6$ physical qubits. We find that fallback-based rotation synthesis methods become a scalability bottleneck: the probability that all $L^2$ parallel rotations succeed on the first attempt vanishes exponentially with system size, causing the failure branch to dominate the expected runtime already at moderate $L$.

We present the quantization of all symmetry reductions of the Einstein--Hilbert Lagrangian that correctly reproduce the reduced Einstein's field equations -- i.e., characterized by the infinitesimal group actions obeying the principle of symmetric criticality. These correspond to the spacetime symmetries of spherical/hyperbolic/planar Schwarzschild/Taub--NUT, BI/BII/BIII-metrics, near-horizon extreme Kerr geometry, swirling universe, closed/open/flat FLRW cosmologies, other FLRW-type metrics, and Bianchi type I, II, VIII, and IX spacetimes. We derive the Hamiltonian and the conformal symmetries of the superspace metrics (the conditional symmetries), promote them to operators, and solve the Wheeler--DeWitt equation with and without imposing these symmetries.

We explore the coincidence of scales between cosmic inflation and right-handed neutrinos in seesaw models. We show that inflation models, which will be tested by next-generation CMB experiments, can produce right-handed neutrinos in sufficient abundance to explain the observed baryon asymmetry of the universe. The model can be tested by gravitational wave signatures from cosmic inflation and particle production.

Measurement-induced phase transitions are nonequilibrium transitions between phases characterized by distinct entanglement scaling behaviors, driven by the competition between unitary dynamics and measurements. Despite recent numerical efforts, how quenched disorder affects these transitions remains unclear. In this work, we study a $d$-dimensional noninteracting fermionic system subject to both quenched disorder and continuous monitoring of the local particle density, and derive an effective field theory describing its long-time universal behaviors. We find that the system is governed by the same nonlinear sigma model as in the case of clean monitored fermions, with disorder entering only through a modification of model parameters. This result suggests that the presence or absence of a measurement-induced phase transition is unaffected by the introduction of disorder: in spatial dimensions d>1, a transition occurs between an area x log law phase and an area law phase, whereas in d=1, the system exhibits only an area law phase and no transition. Numerical results further demonstrate that both clean and disordered one-dimensional free fermions exhibit area-law behavior when the system size is large enough.

The degree of black-hole spin-orbit misalignment ("tilts") in the astrophysical population could be a powerful diagnostic to distinguish between binary formation in isolation, in dynamical environments, or in hierarchical triples. However, robust population-level spin tilt measurements are complicated by model misspecification as well as numerical and Poisson variance, ultimately owing to poor single-event constraints on tilts. Motivated by reports of a possible peak in the spin tilt distribution, we analyze the fourth LIGO-Virgo-KAGRA gravitational-wave transient catalog to test for preferred spin orientations at different black hole masses. We find that a peak in spin tilts is not statistically significant nor model independent. Since the data cannot be used to reliably identify subpopulations based on their spin tilt properties, we also consider a complementary approach: measuring the spin magnitude and tilt distributions at fixed mass scales. We find no confident correlation between mass and spin tilt, but we do confirm a confident correlation between spin magnitude and mass, corroborating recent analyses.

Quantum many-body scars enable persistent non-ergodic dynamics in otherwise thermalizing systems, yet their stabilization typically relies on fine-tuned initial states or engineered Hamiltonian perturbations. Here we show that lattice geometry alone can serve as a powerful and experimentally accessible control knob for inducing and enhancing scarring. By transforming a one-dimensional chain into a quasi-one-dimensional triangle-decorated lattice, we find that the fully polarized state -- normally thermalizing in the PXP model -- exhibits pronounced fidelity revivals, slow entanglement growth, and strong overlap with a tower of weakly entangled eigenstates. We trace this behavior to a geometry-induced restructuring of the constrained Hilbert space, whereby the adjacency graph decomposes into hypercube subgraphs that enforce coherent population transfer and stabilize an emergent approximate $\mathrm{su}(2)$ algebra. We propose a direct implementation in programmable arrays of tweezer-trapped Rydberg atoms, where the triangle-decorated geometry can be realized using spatial light modulators and the resulting scarring dynamics probed via time-resolved measurements of excitation density. Our results establish lattice connectivity as a design principle for engineering non-ergodic dynamics in constrained quantum systems.

We construct an $N=1$ supergravity action whose bosonic part contains an arbitrary function of the scalar curvature, the so-called $F(R)$ gravity. As in $R+R^2$ supergravity, it can be described in terms of two chiral superfields of no-scale supergravity: one contains the scalaron which plays the role of the Starobinsky inflaton and the other contains the goldstone fermion of spontaneously broken supersymmetry during the inflation plateau. Its (complex) scalar component acquires a non-tachyonic mass in the presence of the string dilaton and can be set to zero, together with the pseudoscalar partner of the scalaron, so that the scalar potential is reduced to the one of $F(R)$ gravity. In a perturbative expansion in powers of $R$, one obtains a small deformation of the Starobinsky cosmological model that solves the problem of initial conditions within the validity of the effective field theory, below the scale of tower of states predicted by the swampland distance conjecture. We also show that a particular example of an underlying microscopic theory with such properties is provided by a four-dimensional heterotic string model containing the Standard Model of particle physics.

Conventional approaches to simulating quantum many-body dynamics produce a single trajectory: if the Hamiltonian or the initial state is changed, the computation must be re-performed. Recent efforts toward foundation models have begun to address this limitation, yet existing methods transfer across either Hamiltonians or initial states, but not both. In this work, we introduce the Universal Neural Propagator (UNP), a single, unified model that learns the functional mapping from driving protocols to time-evolution propagators. Trained in an entirely self-supervised way, a single UNP model predicts dynamics across a function space of driving protocols and an exponentially large Hilbert space of initial states simultaneously. We benchmark on a two-dimensional driven Ising model and demonstrate the UNP's accuracy and transferability across product and entangled initial states, as well as for both in- and out-of-distribution driving protocols. The UNP remains accurate at system sizes beyond exact diagonalization, and can be efficiently fine-tuned across all initial states using observable data. By shifting the object of learning from quantum states to operators, this work opens a route toward transferable simulation of driven quantum matter.

Quantum many-body scars in Rydberg atom arrays have thus far only been observed on bipartite lattices, leaving open the question of whether and how they survive frustration, and what the appropriate initial states are that lead to nonthermal dynamics. We introduce a graph-theoretic framework to find suitable candidates for scarring on arbitrary lattices. Our framework predicts two distinct mechanisms: type-I scars generalize the bipartite case by using locally entangled states to overcome mild frustration, while type-II scars exploit strong frustration to pin part of the lattice, leaving the remainder to oscillate freely. We numerically demonstrate both mechanisms and uncover an exponential family of scarred trajectories on the hexagonal lattice that can encode information protected from thermalization. Our results establish scarring as a generic feature of Rydberg systems beyond one dimension and provide an experimentally accessible route to systematically probing non-thermal dynamics in quantum simulators.

We study quantum dynamics generated by time-dependent Hamiltonians in Krylov space, the minimal subspace in which the evolution takes place. We establish a direct link between dynamics in the time-dependent Krylov subspace and the underlying Lie-algebraic structure of the Hamiltonian. We develop a general framework in which the dynamics in the time-dependent Krylov subspace is generated by ladder operators of the associated Lie algebra. In particular, we identify the minimal conditions under which the exact time-dependent Krylov dynamics is naturally determined by the interaction-picture Hamiltonian and governed by an embedded $\mathfrak{sl}(2,\mathbb{C})$ subalgebra. We further show that an exact single-exponential representation of the time-evolution operator gives rise to a distinct time-independent Krylov dynamics in a unitarily related basis, from which the exact time-dependent Krylov dynamics can nevertheless be recovered. We also extend the framework to the oscillator algebra as the simplest extension of the nilpotent Heisenberg--Weyl algebra, and provide further examples, including the translated and dilated harmonic oscillator, systems governed by closed Virasoro subalgebras, a spin in a rotating magnetic field, and higher-dimensional generalizations for multi-level systems. In addition, we introduce a new quantum speed limit to the complexity growth rate generated by a time-dependent generator and show that, for evolutions governed by a Lie algebra, it retains the same functional form as in the time-independent case. Remarkably, saturation of this bound is strongly affected by temporal driving and persists only when the Hamiltonian commutes with itself at different times. These results establish a unified framework for characterizing operator growth and Krylov complexity in time-dependent quantum systems with underlying Lie-algebraic structures.

Strong-to-weak spontaneous symmetry breaking (SWSSB) is diagnosed by nonlinear correlators, but its direct static implication for conserved charge fluctuations is not automatic. We show that, for continuous symmetries, long-range Rényi-1 correlator, together with a sufficiently rapid approach to its nonzero asymptotic value, forces subsystem charge indefiniteness: the block-charge variance has an extensive lower bound; equivalently, the truncated symmetry expectation has extensive curvature. This gives a precise static fluctuation footprint of charge scrambling. We construct examples to show that the implication is conditional and non-reversible: dephased superfluids retain Rényi-1 SWSSB with subextensive charge variance when the Rényi-1 tail is too slow, while sparse fixed-charge projectors have extensive charge variance but no local charge-transfer Rényi-1 order or long-range conditional mutual information. Finally, we introduce a \emph{twist overlap} correlator, which serves as an analogue of charge variance applicable to both discrete and continuous symmetries. This naturally decomposes local block-charge fluctuations into strong- and weak-symmetry channels. We found that the weak-symmetry channel isolates coherent charge fluctuations and is directly related to the Wigner--Yanase skew information. Taken together, these results give a unified understanding for distinguishing nonlinear SWSSB order, local charge indefiniteness, and coherent charge fluctuations.

Electro-optic modulation is central to classical optical communications and emerging quantum technologies. High-confinement optomechanical crystal modulators enable microwave-optical transduction through strong optomechanical interactions and offer a promising interface between superconducting qubits and optical fibers. However, their performance is limited by thermal noise from optical absorption. Release-free optomechanical crystals provide improved thermal anchoring but have not yet been integrated into a microwave-optical transducer. Here, we demonstrate a release-free electro-optomechanical transducer combining strong optomechanical interactions in silicon with the efficient piezoelectricity of lithium niobate via micro-transfer printing. We observe electro- and optomechanical coupling rates compatible with quantum-level operation when co-integrated with a superconducting microwave circuit. This advance moves release-free electro-optomechanical devices toward practical microwave-optical interfaces.

We consider the supersymmetric solutions of several supergravity theories (ungauged $\mathcal{N}=2,d=4$ and $\mathcal{N}=1,d=5$ supergravities coupled to vector supermultiplets and pure $\mathcal{N}=1,d=10$ supergravity) and show that their generalized Komar charges vanish identically for the supersymmetric Killing vector which is constructed as a bilinear of the Killing spinors of those solutions. This property can be used to prove the supersymmetry (``BPS'') bounds satisfied by some of those solutions in a rigorous, coordinate-independent way.

We simulate the effects of a neutral electron--hole plasma on Rydberg excitons in cuprous oxide (Cu$_2$O), focusing on the validity of Debye screening and the role of plasma-induced thermalization. Unlike atomic Rydberg states, excitons in Cu$_2$O consist of quasiparticles with comparable effective masses whose orbital frequencies can exceed the plasma frequency, invalidating the assumption of a stationary screened charge. Using two complementary approaches, a classical orbit model and a harmonic-oscillator representation evolved via the truncated Wigner approximation, we study exciton lifetimes and interaction screening under realistic plasma conditions. We find numerically that plasma-induced scattering induces finite exciton lifetimes with specific scaling relations with plasma density, principal quantum number $n$ and temperature, possibly providing an explanation for experimentally observed deviations from the $n^3$ scaling at high principal quantum numbers. By explicitly computing time-averaged electric fields, we show that Debye screening overestimates the screening of the exciton's internal field, especially for high angular momentum states. Furthermore, we demonstrate that exciton-exciton interactions are not Debye screened at separations comparable to the Debye length for Rydberg excitons that are well resolvable in absorption measurements.

Absolutely Maximally Entangled (AME) states are important resources in quantum information processing; however, a general systematic approach for constructing these states remains a formidable challenge. We identify a finite-field rank structure underlying multipartite entanglement in a class of quadratic-phase quantum states defined by symmetric matrices over $\mathbb{F}_p$. We prove an exact Rank-Purity Duality: the Rényi-2 purity of any subsystem is determined solely by the rank of the phase matrix. Within this ansatz, the existence of an AME state is equivalent to the existence of a generating phase matrix $P$ whose bipartition submatrices are of full rank, reducing the condition for maximal entanglement to a rank constraint on $P$. This establishes a direct correspondence between entanglement and cut-rank geometry in finite-field matrices. Furthermore, for square-free local dimensions, we show that the entanglement structure factorises via the Chinese Remainder Theorem into independent prime-field contributions, yielding an exact additive decomposition of Rényi-2 entropies. These results provide an algebraic characterisation of entanglement in the quadratic phase formalism and enable the systematic construction of highly entangled states.

Across many areas of science, there is a need to generate magnetic fields that are both ultra-stable and switchable on and off. While permanent and superconducting magnets offer exceptionally low-noise fields, they are not readily switchable. Conversely, electromagnets are switchable but are susceptible to current noise. We present a hybrid technique to switch the field of any arbitrary magnet through use of a non-linear ferromagnetic circuit, named the Saturable Electronic Reluctance Switch (SERS). The circuit achieves bi-stable switching of the field by applying a current above a given threshold, akin to a transistor for magnetic fields. Crucially, the applied current has minimal influence on the magnetic field output and demagnetisation of the magnet is avoided, drastically reducing power dissipation. SERS is also robust to fabrication errors, suppressing noise in the control current by several orders of magnitude in a non-ideal device. To illustrate its application, a SERS-driven device is proposed for generating ultra-stable magnetic field gradients in a scalable trapped-ion quantum computer. We find this device offers an order of magnitude reduction in power dissipation compared to state-of-the-art current carrying wires, while reducing magnetic field noise originating from current fluctuations by up to five orders of magnitude.

Observing non-Gaussianity in the timing residuals of Pulsar Timing Arrays (PTAs) has recently attracted attention as a potential discriminator between astrophysical and cosmological origins of the observed Gravitational Wave (GW) signal. In this work, we show that even in an idealized signal-dominated setup, after decorrelating data to avoid spurious detections, statistical tests applied to PTA data cannot distinguish between Gaussian and non-Gaussian GWBs in a model-agnostic way. In particular, without making strong assumptions on the GW spectrum or the properties of the population, the sensitivity to any distinctive non-Gaussian feature is washed out.

In this paper, we illustrate how a Schrödinger cat state created via a matter-wave interferometer can be viewed as the simplest quantum-gravity setup where we can treat both matter and gravity on an equal footing at a perturbative level. Here we treat Einstein's theory of general relativity using an effective field theory approach, quantising the massless spin-2 graviton in the presence of a quantum spatial superposition of matter that creates a matter-wave interferometer in the non-relativistic limit. We show that due to the matter-graviton coupling the graviton vacuum is displaced analogous to the coherent state. We study the contrast/overlap between the coherent states of the left and right superpositions in the matter-wave interferometer. We also study the entanglement between matter and the graviton in this setup and relate it to a gravitational contrast, or the overlap of the quantum geometries led by the coherent states. In the appendix, we provide an example of a time-dependent harmonic oscillator and study the contrast/overlap of such coherent states of the graviton.

For CSS syndrome decoding, the two check matrices impose binary parity-check constraints on the two Pauli error components. The posterior can therefore be written as a binary factor graph with two Tanner graphs coupled by the local joint prior at each qubit. We call the sum-product algorithm on this factorization joint belief propagation (joint BP). Joint BP retains the local channel correlation between the two Pauli components. This note compares joint BP with the four-state Pauli-label factor graph used for four-state BP. The two algorithms are shown to have the same posterior weights, messages, and beliefs after relabeling the four local Pauli states and marginalizing the irrelevant binary component.

We present an exact black hole solution in anti-de Sitter (AdS) spacetime with a Kalb-Ramond field coupled to nonlinear electrodynamics (NLED), characterized by mass, magnetic monopole charge, and Lorentz-violating parameters. The geometry admits two horizons (inner and outer) that coalesce into a degenerate horizon at a critical monopole charge. Beyond this critical point, no black hole solutions exist. In the limit of vanishing Lorentz-violating parameters, the solution reduces to the modified Kalb-Ramond and Bardeen black holes, while suitable parameter choices reproduce the Reissner-Nordström-AdS and Schwarzschild-AdS geometries. We analyze the thermodynamics of the solution by computing the Hawking temperature, entropy, specific heat, and Gibbs free energy. The NLED source introduces nontrivial modifications: the Hawking temperature displays nonmonotonic behavior with possible local extrema, the entropy deviates from the standard area law, and the specific heat may assume negative values, signaling thermodynamic instabilities. The Gibbs free energy exhibits swallow-tail structures, indicative of first-order phase transitions. Furthermore, we derive the first law of black hole thermodynamics in the extended phase space, together with the Smarr relation, and confirm their validity for the Kalb-Ramond black holes with NLED sources. Our findings highlight the rich thermodynamic structure induced by Lorentz-violating effects and nonlinear electrodynamics in AdS black hole backgrounds.

Motivated by the indications of time-varying dark energy equation of state reported from DESI, we investigate a quintessence model with an exponential potential $V_0 e^{-λφ/m_{\mathrm{pl}}}$. We derive an analytical relationship between the current equation of state parameter for the quintessence field and the potential parameter $λ$ required to realize sufficient duration of radiation and matter domination. Our results provide a useful analytical relation for inferring the potential parameter $λ$ from the observed current equation of state parameter. Furthermore, based on this framework, we provide a new analytical upper bound on the potential parameter $λ$ for current accelerated expansion. Concretely, we obtain $λ<1.94$ by adopting $Ω_{\phi0}=0.685$.

In this work, we explore the dynamics of quantum correlations, namely coherence, entanglement, and nonlocality associated with a Bell state, in a dimeric arrangement of organic PBI molecules, mediated by dipole-dipole interactions, under time-fractional dynamics. Within the framework of the time-fractional Schrödinger equation (TFSE) with Caputo fractional derivatives, we explore system dynamics for different values of the fractional order $τ$, transition energies, interaction strength, and purity $p$. We employ the relative entropy of coherence, logarithmic entanglement entropy and concurrence, and CHSH inequality to estimate system dynamics associated with coherence, entanglement, and nonlocality, respectively. These findings highlight the role of the fractional order $τ$ in system dynamics, including memory effects and relaxation, and thereby bring together ideas from fractional calculus and quantum information theory perspectives and discuss methodologies to control and utilize these molecular quantum correlations.

When a quantum system exhibiting a second order phase transition is quenched across the critical point in large but finite time, the dynamics are not adiabatic in the critical region and the Kibble-Zurek (KZ) mechanism provides a framework to determine local observables such as the mean defect density. However, to find higher-point functions, one has to go beyond the KZ paradigm asshown in recent works on one-dimensional transverse field Ising model (TFIM) following a linear quench. It has been found that (i) besides the KZ scale, the quench dynamics depend on another length scale that arises due to the finite phase difference between the low energy modes, and (ii) contrary to the expectations based on the KZ mechanism, in general, the correlation functions do not decay exponentially with distance. Motivated by these results for the linear quench, we are interested in understanding if these properties are universal, and consider the 1D TFIM when the transverse field varies algebraically in the vicinity of the critical field. We focus on the equal-time,longitudinal kink-kink correlation function at the end of the quench from the paramagnetic to the ferromagnetic phase, and find that (i) the correlator depends only on the KZ length for superlinear quenches, otherwise an additional dephasing length is required to describe it, and (ii) the dephased correlator decays as a compressed exponential with an exponent that changes continuously with the quench exponent. Our results are obtained using an adiabatic perturbation theory, analytical arguments and exact numerical integration of the relevant equations.

We develop a local reconstruction framework between $Φ(R,φ,X)$ theories with linear dependence on $X$ and generalized hybrid metric--Palatini gravity. The construction is formulated in vacuum in the Einstein frame, where both formulations can be written as two-scalar theories with the same field-space geometry. The framework provides a practical method for finding $Φ(R,φ,X)$ and $f(R,\mathcal R)$ functions that describe the same regular Einstein-frame two-scalar sector. Starting from a given $Φ(R,φ,X)$ model, we derive the equation that determines the compatible hybrid functions $f(R,\mathcal R)$ and show that it has a Clairaut-type structure. We also show that the inverse reconstruction is not unique: a regular hybrid Einstein-frame potential determines a family of compatible $Φ(R,φ,X)$ theories, parametrized by the kinetic coupling. Explicit examples illustrate the reconstruction procedure, its domain of validity, and the translation of model parameters between the $Φ(R,φ,X)$ and $f(R,\mathcal R)$ formulations.

We analyze permutation routing of rigid blocks representing surface code patches of $d_C^2$ atoms on a reconfigurable lattice with hypergraph transformations. For a hypergraph $H$, code distance $d_C$, $s=d_C^2$, number of blocks $N_L$, and guard distance $g$, we show the block routing number $\mathrm{rt}_B(H, s, g) = Θ(d_C \log N_L)$. A spectral analysis of the quotient graph $Q(G_{\mathrm{cl}}(H), B)$ (blocks as supervertices) shows that the spectral ratio $β_Q < 1$ is preserved in the high-connectivity regime. Negative association of block permutations and congestion bounds are used for random intermediate configurations. Serialization establishes that each quotient routing phase requires $O(d_C)$ physical sub-steps due to the block footprint width. A lower bound $\mathrm{rt}_B = Ω(d_C \log N_L)$ follows from combining the spectral lower bound on quotient phases with the traversal cost per phase. We include error model analysis grounded in recent experimental results, syndrome extraction protocols (stop-and-correct, rolling active fault-tolerant (AFT) measurement, and adaptive deformation), and integration with lattice surgery compilation via the Litinski protocol. Composition with the correlated-decoding scheme reduces syndrome-extraction overhead from $O(d_C)$ to $O(1)$ per correction window, leaving routing as the leading-order contributor to the integrated $O(d_C \log N_L)$ depth. Spectral inheritance is organized in a hierarchy: exact (Haemers interlacing on equitable partitions), perturbative (Weyl bounds for near-equitable partitions, a practically relevant case for surface-code patches), and universal (higher-order Cheeger). Methods extend directly to QCCD trapped-ion architectures under the same regime condition, with junction crossings replacing AOD transports as the elementary single-hop translation.

We investigate the dynamical and spectral consequences of capacitance-network-mediated interactions in superconducting transmon arrays beyond effective nearest-neighbor descriptions. While weak coupling regimes are well captured by an effective nearest-neighbor interacting models, we show that increasing capacitive connectivity induces a pronounced departure from this approximation in dynamical observables. Using Out-of-Time-Ordered Correlators (OTOCs), we demonstrate that such network-mediated couplings significantly accelerate operator scrambling, leading to rapid saturation compared to the nearest-neighbor limit. This dynamical crossover is accompanied by a shift in spectral statistics away from Poissonian behavior toward level repulsion, with the ratio parameter remaining intermediate between Poisson and Gaussian Orthogonal Ensemble (GOE) limits. This indicates the emergence of partial ergodicity rather than fully developed quantum chaos. As this behavior arises within experimentally realistic regimes of current superconducting transmon devices, identifying when network-mediated couplings qualitatively alter information dynamics is directly relevant for scalable superconducting architectures.

We present a Fisher-matrix forecast for the detectability of a stochastic gravitational wave background generated by a first-order phase transition in the early universe. We use the DECIGO and LISA missions as reference cases. The source gravitational wave spectrum $Ω_{\rm GW}(f)$ is modeled as the sum of sound wave and turbulence contributions and is parameterized by the transition strength $α$, its inverse duration $β/H_*$, its transition temperature $T_{*}$, and the bubble wall velocity $v_{w}$. For each detector, we construct fiducial models with signal peaking in the sensitivity band of the detector, fixing $T_{*}$ and $v_{w}$, and perform a Fisher analysis on the remaining parameters $\lnα$ and $\ln(β/H_{*})$. A two-parameter Fisher analysis in $\{\lnα,\ln(β/H_{*})\}$, with fixed values of $T_{*}$ and $v_{w}$, yields marginalized $1σ$ uncertainties $σ(\lnα)\simeq 0.12$ and $σ[\ln(β/H_{*})]\simeq 0.145$. The parameters are strongly correlated, with correlation coefficient $\mathrm{corr}\simeq 0.98$. We perform a corresponding analysis for LISA and report marginalized $1σ$ uncertainties $Δα/α\simeq {}^{+0.044}_{-0.042}$ and $Δ(β/H_{*})/(β/H_{*}) \simeq {}^{+0.119}_{-0.107}$, with correlation coefficient $\mathrm{corr}\simeq 0.78$.

This work presents polarization-selective photon-magnon coupling (PMC) in a planar cavity-magnonic platform consisting of an electric-LC resonator (ELCR) side-coupled to a microstrip transmission line and integrated with a yttrium iron garnet (YIG) thin film. The ELCR supports two orthogonal photon modes at $\sim 3.93$ GHz and $\sim 5.73$ GHz, whose excitation and radiative damping are governed by the resonator orientation relative to the microwave-field polarization. Rotating the resonator enables controlled switching between these modes and tunable photon-magnon hybridization. An equivalent circuit model including intrinsic and extrinsic damping successfully reproduces the polarization-driven mode switching, while an effective three-mode Hamiltonian accurately captures the coupled-mode evolution. The results reveal strong angular tunability of the PMC strength through redistribution between two competing interaction channels. At $θ= 0^\circ$, only the lower-frequency photon mode is excited, yielding $g_{31}=56.5$ MHz, while the higher-frequency mode remains inactive. As the angle increases, both channels become active: $g_{31}$ increases from $56.5$ to $98$ MHz over $0^\circ$-$60^\circ$ before vanishing at $90^\circ$, whereas $g_{23}$ decreases from $76$ to $30$ MHz over $30^\circ$-$90^\circ$. The observed evolution yields a measured transition near $25.7^\circ$ and a symmetry-related model-predicted transition near $154.3^\circ$. These findings establish resonator-orientation--driven polarization selectivity as a versatile mechanism for controllable photon--magnon interactions in planar architectures.

Neutrino oscillations confirm the presence of mode entanglement, as each flavor eigenstate is composed of a coherent superposition of distinct mass eigenstates. In this work, we investigate the dynamics of quantum resources in neutrino oscillation systems by analyzing quantum steering, logarithmic negativity, and quantum coherence within a two-flavor framework. Treating neutrino oscillations as an effective two-level quantum system, we study the influence of environmental decoherence on these nonclassical features by modeling the system as an open quantum system. Three representative noise channels are considered, namely amplitude damping (AD), phase flip (PF), and phase damping (PD), allowing us to capture both dissipative and dephasing mechanisms. We examine the evolution of quantum resources in both Markovian and non-Markovian regimes, highlighting the role of memory effects in the system-environment interaction. The results reveal a clear hierarchy in the robustness of quantum resources under decoherence. Steering is the most sensitive correlation in the hierarchy under decoherence effects. while logarithmic negativity exhibits intermediate robustness. Quantum coherence displays the highest resilience, persisting over a wider range of parameters. In the PF and PD channels, logarithmic negativity and coherence are shown to exhibit identical dynamical behavior, reflecting their common dependence on phase-related noise. In contrast, the non-Markovian regime leads to delayed decoherence and partial revivals of entanglement and coherence due to information backflow, whereas quantum steering remains strongly suppressed. These findings provide a comparison of different quantum resources in neutrino oscillation systems and offer new insights into the interplay between decoherence mechanisms and quantum correlations.

The construction of a traversable wormhole with double-trace deformation has been achieved so far by using boson fields as the perturbation. In this work, we study double-trace deformation with fermion fields in the two-sided Kerr background to open a traversable wormhole. We construct the fermionic double-trace deformation within the Kerr/CFT framework. We consider the near-horizon, near-extremal Kerr geometry, which is dual to a conformal field theory. The lack of fermionic superradiance let us describe the wormhole at every region, even at the off-axis region where bosonic field experiences instability due to superradiance. By choosing a certain coupling between the left and right boundaries, the two-point function is modified, and its first order correction contributes the negative energy to open the wormhole. The wormhole is most traversable when the perturbation is turned on at early times, with opening that depends on the mode's frequency, the black hole temperature, and the fermion mass. At late times, the average null energy has damped oscillation behavior until eventually reaches zero. Wormhole with lower temperature have less traversability and it is completely closed at extreme limit. On the other hand, rotation near extreme limit can increases the upper bound on information transfer up to the order of the entropy. Additionally, symmetrical effective potential bumps connected by the wormhole can produce observable echoes. We find that the echo time delay cannot exceed the scrambling time of the black hole.

We investigate the propagation of massless fields with spins $s=0$, $s=1$, and $s=1/2$ in the spacetime of an Euler-Heisenberg (EH) black hole surrounded by perfect fluid dark matter (PFDM). This background incorporates both the nonlinear electrodynamic correction associated with the EH effective theory and the logarithmic contribution induced by the surrounding dark matter distribution. After deriving the corresponding Schrödinger-like radial equations, we construct the effective potentials for scalar, electromagnetic, and Dirac perturbations and analyze how they are modified by the black hole charge, the EH parameter, and the PFDM parameter. The greybody factors are estimated through the rigorous Boonserm-Visser lower-bound method, and the associated partial absorption cross sections are obtained for different spin sectors using these bounds. Our results show that the nonlinear electrodynamic and dark matter parameters significantly deform the effective potential barrier, leading to potentially distinguishable changes in the transmission probabilities and absorption spectra within the model. In particular, the greybody lower bounds increase monotonically with the frequency and approach the high-frequency limit, while their low-frequency behavior is strongly affected by the geometry and by the spin of the perturbing field. Moreover, we utilize the greybody lower bound to calculate the energy emission rate. Finally, we make comparisons with the Schwarzschild, Reissner-Nordström, and pure EH limits, showing that the combined EH+PFDM background produces distinguishable corrections to black-hole scattering within the model. These results highlight greybody bounds as sensitive diagnostic probes of nonlinear electrodynamic effects and dark matter halos around compact objects.

Reservoir computing provides an alternative to recurrent neural networks by overcoming the common problems of backpropagation through time and by training only a simple readout layer. The emerging field of quantum computing offers a new computing paradigm that promises to enhance learning through richer feature representations. In this work, we investigate quantum reservoir computing for time-series forecasting. We explore and benchmark four different architectures that combine single or multiple (distributed) reservoirs with single or multiple (distributed) ridge-regression readout layers. We evaluate these architectures using ideal and hardware-informed noisy simulations, and include both hybrid and fully quantum variants, with classical reservoir counterparts serving as a baseline. The results indicate that quantum-enhanced configurations consistently improve forecasting accuracy by reducing the mean absolute error (MAE) and the root mean squared error (RMSE) up to 78.8% and 72.3%, respectively, while distributed architectures effectively enable scaling by utilizing multiple quantum resources in a hardware-agnostic manner. These findings support distributed quantum reservoir computing as a promising, modular approach for forecasting on the quantum platforms of the noisy intermediate-scale quantum (NISQ) era.

The accurate identification of faulty hardware is a fundamental requirement for reliable quantum information processing. We address this problem in a quantum setting, where a series of $n$ devices is intended to apply the same unitary operation, but $k$ malfunctioning devices among them apply a different, unknown unitary action. Under the assumption of complete ignorance regarding the specific unitary transformation applied, we model our hypotheses using representation-theoretic tools and study the zero-error protocol for identifying these faulty devices. We derive the optimal success probability for the single- and two-anomaly scenarios, demonstrating that it is independent of the total number of devices in the series. Furthermore, we present a simple protocol that makes use of ancillary systems that achieves this optimal limit. Notably, this protocol offers significant operational advantages, such as allowing us to test each device independently. Finally, we extend our analysis to the general scenario in which both the number of anomalies and the local dimension of the systems are arbitrary, evaluating our protocol's performance and conjecturing its global optimality in the general case.

We propose a simple ansatz to construct exact wave solutions of the sourceless SU(2) Yang-Mills equations in (3+1) dimensions. The ansatz employs a $y$-dependent rotated Pauli basis and assumes a phase $θ=kz-ωt$ dependence for the gauge potentials. Owing to this ansatz, the nonlinear field equations reduce to nine algebraic constraints, whose complete solution yields three families of exact waves. Family I describes linear (Abelian) electromagnetic waves embedded in the non-Abelian theory; all commutator terms vanish and the dispersion relation is $ω=kc$. Family II represents genuinely nonlinear self-interacting waves that also propagate at the speed of light but exhibit a constant field offset, nonvanishing commutators, and do not obey superposition. The constant offset is gauge-invariant and gives rise to a non-zero time-averaged color-electric field. The energy density has nodes whose position ($θ=0$ or $θ=π$) is controlled by a discrete topological parameter $ξη=\pm1$, providing an observable signature. Family III is a pure gauge solution with vanishing field strengths, valid for arbitrary $k$ and $ω$ without any dispersion relation. All solutions are closed-form and provide new insights into how non-Abelian self-interactions fundamentally alter wave propagation.

Airborne magnetometry requires rigorous calibration to isolate geomagnetic signals from sensor errors and platform magnetic fields. This magnetic compensation is needed for applications like geophysical exploration and magnetic anomaly navigation. The standard approach utilizes a quantum scalar Optically Pumped Magnetometer (OPM) and a less sensitive fluxgate vector sensor for attitude information. This configuration typically results in a scalar approximation of the platform field. Advancements in high-sensitivity Diamond Nitrogen-Vacancy (NV) vector magnetometers now enable a re-evaluation of the standard hardware configuration and full vector calibration models. We show through rigorous theoretical analysis that scalar calibration models are robust to misalignment. Vector calibration models, however, are intrinsically first-order sensitive to attitude errors, irrespective of the accuracy of the magnetic field measurements. These errors arise from inaccurate representation of the background field direction in the body frame, and can amplify small orientation errors into noticeable calibration residuals. Using realistic sensor models and flight trajectories, we evaluate different sensor configurations for magnetic calibration and assess the use of onboard Inertial Navigation Systems (INS) as an independent attitude reference to enable stable compensation. Our results suggest that quantum vector magnetometers like NV sensors are not sufficient to solve the attitude bottleneck for airborne vector magnetic calibration. However, as a single sensor capable of providing both absolute field and directional measurements, they may offer benefits regarding sensor placement, synchronization, and scalar calibration accuracy.

In the domain of variational quantum algorithms, quantum Fourier models (QFMs) provide a mathematically well defined structure for quantum machine learning (QML). There has been a substantial amount of work on the scalability and trainability of such models showcasing the potential but also the limitations for the prospective application of QFMs. However, much less is known in the context of pulse-level quantum computing, where the microwave parameters that implement unitary operations on the hardware are used to perform computations directly instead of through the interface of quantum circuits. In this work, we evaluate QFMs through the lens of pulse parameters and link metrics such as expressibility and Fourier coefficient correlation (FCC) to this extended set of variational parameters. We show that while control over pulse shapes does not significantly alter the global expressibility or structural correlations of the Ansatz, it fundamentally alters the local optimisation landscape. For composite gates, independent pulse scalings replace a single logical angle by multiple independently tunable sub-angles. This relaxes the rigid monomial couplings induced by the gate-level parameterisation, and provides gradient descent with higher-dimensional escape routes, decoupling local parameter constraints and significantly boosting performance during training. Following an analytical proof, we show numerical results validating our theory on training a QFM with an exponential (ternary) feature map on a Fourier series with the same frequencies.

The classification of general probabilistic theories (GPTs) whose CHSH value is stable under arbitrary rounds of teleportation and entanglement swapping was recently obtained in Dmello and Gross work and consists of seven families, indexed by characters of the Klein four-group $K_4$, the cyclic group $\mathbb{Z}_4$, and the dihedral group $D_4$. The question of which of these families admits a realization within standard quantum mechanics was left open. In this work we resolve this question completely. Using elementary representation theory, we prove that exactly two families are quantum-realizable, namely $χ^{K_4}_{1234}$ and $χ^{D_4}_{125}$, while the remaining five admit no quantum realization.

In this paper, we investigate the thermodynamic and radiative properties of a regular black hole sourced by primordial dark matter (PDM), modeled effectively through a Dirac--Born--Infeld (DBI) scalar field. We compute the Hawking temperature, the entropy obtained from the first law at fixed PDM scale, the specific heat capacity, the sparsity parameter of the Hawking flux, and the spectral energy emission rate. Particular attention is devoted to the role played by the regularity scale parameter \(α\) and to the recovery of the Schwarzschild limit. Using the normalization in which the integration constant \(M\) is the ADM mass and \(f(r)=1-2M/r+\mathcal{O}(r^{-3})\), we find that the PDM scale suppresses the Hawking temperature and the spectral energy emission rate relative to the Schwarzschild case. The fixed-\(α\) heat capacity remains negative along the physical branch, indicating the persistence of local thermodynamic instability in the canonical ensemble. Moreover, within the effective-area prescription adopted here, the geometrical sparsity parameter receives a negative leading correction in the perturbative regime \(α\ll 2M\), implying a slight reduction of the intermittency of the Hawking flux. We also distinguish between the near-horizon geometrical estimate and the shadow-based high-energy absorption cross-section used in the emission rate.

We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a compact, convex set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test that adaptively selects measurements based on the current mixture estimate of the alternative set, and stops upon the first threshold crossing of the mixture log-likelihood ratio. Under an expected sample size constraint, we show that our proposed adaptive strategy simultaneously achieves the optimal Type-I and (worst-case) Type-II error exponents. These exponents are characterized by the minimal measured relative entropies between the null state and the alternative set. We further establish a matching converse, thereby characterizing the optimal error exponent region. Finally, our results show that achieving vanishing error probabilities in composite SQHT requires an expected sample complexity at least as large as that of sequential testing between two fixed quantum states.

Spin squeezing can suppress quantum projection noise via interparticle entanglement, therefore enabling measurement sensitivities beyond the standard quantum limit. In practice, however, the Gaussian and finite intensity profiles of the optical probe beam induce spatially inhomogeneous atom-light interactions. As polarized atoms move within a vapor cell, they experience position-dependent optical intensities, generating transit noise that limits spin squeezing performance. Here, we investigate the transit noise in a coated rubidium vapor cell through combined theoretical analysis and experimental measurements. By varying the probe beam diameter, we quantify the dependence of transit noise on beam size and atomic Larmor frequency. Our results show that, for a vapor cell with fixed dimensions, the transit noise increases as the probe beam spot area decreases. Moreover, when the Larmor frequency is below the characteristic linewidth of the transit noise, the noise contribution becomes larger. We further calculated and measured spin squeezing for different beam sizes and found an experimental difference of $2.7 \pm 0.2$ dB between 2~mm and 0.6~mm, similar to the theoretical prediction of $3.0 \pm 0.3$ dB. Theoretical analysis under conditions of stronger squeezing shows that transit noise becomes an even more critical limiting factor. These results provide practical guidance for optimizing probe beam parameters and suppressing transit noise in spin squeezing experiments.

Quantum error correction (QEC) is essential for achieving low error rates required for fault-tolerant quantum computation. In stabilizer-based codes such as the surface code, errors are inferred from repeated syndrome measurements and corrected by a classical decoder. To prevent error accumulation, decoding must be performed with both high throughput and low latency to keep pace with the QEC cycle and enable real-time feedback for universal logical operations. Here we report a hardware-integrated control architecture featuring an FPGA-based neural-network (NN) decoder and experimentally demonstrate real-time surface-code (distance-3) QEC on a superconducting quantum processor. The system achieves a deterministic closed-loop latency of 550 ns, including 124 ns for NN decoding, enabling feedback corrections within a 1.25 us QEC cycle. We show that real-time decoding and feedback correction achieve logical performance comparable to offline decoding while maintaining robustness against varying error conditions. We further demonstrate mid-circuit feedback correction in non-Clifford logical circuits, where Pauli-frame updating alone becomes insufficient. Our results establish a low-latency hardware architecture for embedded QEC control and provide a pathway towards scalable fault-tolerant quantum computing systems.

Entanglement is a key quantum resource in various quantum protocols, with a rich set of laws governing its manipulation. In this context, catalysis refers to the possibility of an auxiliary state that enables a previously forbidden manipulation, while being completely returned at the end. While the catalytic setting has been thoroughly examined in the single-copy regime, much less is known in the asymptotically many copy regime. In this work, we focus on the entanglement cost of preparing asymptotically many copies of a given state exactly. We show that catalysis can significantly lower the exact entanglement cost by constructing an explicit catalytic protocol. Additionally, these findings generalize readily to other resource theories, showing a general catalytic advantage in the resource dilution task.

We present the construction of efficient linear-combination-of-unitaries (LCU)-based block-encodings for the first-order derivative and Laplacian operators in the SLAC representation. We use state-preparation techniques designed for smoothly decaying functions to efficiently prepare the dense LCU amplitudes with high success probability and low gate cost. Furthermore, we demonstrate how Shannon wavelet transforms can be applied to these block-encodings to efficiently obtain multi-scale representations of the SLAC derivative operators. We then show how to apply a diagonal preconditioner that reduces the condition number of these matrices in the multi-scale wavelet basis to a small constant. This approach enables the solution of partial differential equations with SLAC-discretised derivative operators on a finite lattice using the quantum linear solving algorithm (QLSA). Throughout this work, we analyse the computational complexity and error scaling of each implementation.

We study the class of edge-coloured graphs arising from the graph-theoretic representation of quantum photonic experiments that generate multipartite W-states. Abstracting away physical amplitudes and phases, we introduce W-state graphs: matching-covered graphs equipped with a half-edge 2-colouring such that every perfect matching contains exactly one bichromatic edge and every vertex is incident with a red half-edge. Our main contribution is a complete structural characterization of W-state graphs. We show that a graph is a W-state graph if and only if each of its 3-connected components is a W-cone, a simple and rigid building block defined by a universal vertex and a factor-critical base. This characterization implies that no W-state graph is simple and yields a recognition algorithm running as fast as verifying whether a graph is matching-covered. We also show that the natural generalization to Dicke states encounters a complexity barrier: verifying one of the two Dicke state conditions is itself coNP-complete, resolving an open problem of Vardi and Zhang [IJCAI 2023]. Our results place W-state graphs firmly within classical matching theory and precisely delineate the combinatorial structures capable of realizing idealized W-states in the experiment-graph framework.

Primordial black holes (PBHs) can be produced from inflation if the primordial curvature power spectrum is strongly enhanced on scales much shorter than those probed by cosmic microwave background (CMB) experiments. In single-field models this typically requires a transient departure from slow-roll, attractor dynamics, for example realized through a brief ultra-slow-roll phase. In these scenarios, there is reasonable concern that large-scale modes, whose statistics is tightly constrained by CMB observations, might back-react to the amplified perturbations on much shorter scales. In a perturbative expansion for the long-mode power spectrum, this effect first appears at 1-loop. In these proceedings we summarize recent works on this issue, based on the application of the separate-universe framework and its general extension with multi-point propagators. We show that back-reaction at 1-loop is due to either (i) non-linear super-horizon evolution, or (ii) 1-loop-corrected initial conditions. By assuming separation of scales and adiabaticity of the long mode, we show that the 1-loop back-reaction is not observable and large scales decouple from enhanced short ones. While we demonstrate that PBH production within single-field inflation does not disrupt large-scale predictions, we close by discussing scenarios to which our results do not apply.

We generalize proper scoring rules to the quantum domain, replacing probability distributions with density operators. We define Quantum Value Functionals via operator convex generators and establish a complete duality theory yielding proper quantum scoring rules. We derive minimax optimal bounds for quantum state tomography under McCarthy-type incentives, proving a Quantum Cramér-Rao-McCarthy Bound that explicitly links minimax risk to the curvature of the generating function and the Quantum Fisher Information. We quantify the economic value of quantum resources (coherence, entanglement, adaptivity) in forecasting tasks, establishing scaling separations between classical and quantum estimation strategies. Our results guide the design of quantum sensors, incentive-compatible quantum data markets, and robust quantum machine learning protocols.

This paper addresses resource allocation for entanglement distribution in multi-channel quantum networks. A system model is proposed that integrates a multi-channel quantum network architecture with heterogeneous link characteristics and user-centric entanglement request handling, including queuing and retry mechanisms. Classical allocation methods for assigning channels and quantum processors to generate entanglement between end nodes are implemented, including the Dynamic Efficient algorithm, Static Efficient algorithm, and the Success Enhancement algorithm. In addition, a Proximal Policy Optimization (PPO)-based allocation approach driven by a reward function is proposed. These methods are evaluated through multi-slot simulations using metrics such as request delay, total number of successful entanglement requests, network capacity utilization, and the entanglement request handling rate. The results show that Dynamic Efficient achieves the lowest delay, while Success Enhancement improves the number of successful requests through multipath allocation. The PPO-based method provides the best overall balance by improving capacity utilization and achieving both low delay and a high number of successful entanglement requests.

We address the circuit-design problem of maximizing quantum magic in early fault-tolerant quantum computing (early FTQC), where logical dynamics natively take the form of alternating Clifford layers and diagonal non-Clifford layers. To render this optimization analytically tractable, we first prove a uniqueness theorem: for operational magic functionals built from Pauli expectation values, the axioms of faithfulness and tensor-product additivity force a Rényi-type dependence on the Pauli-spectrum. Leveraging the closed phase-polynomial description of the diagonal Clifford hierarchy, we derive exact Pauli-spectrum expressions and tight bounds for a shallow-layer model. These bounds expose a zero-magic mechanism and prove that maximal magic strictly requires graph-state preconditioning. Consequently, we establish our first no-go theorem: hierarchy level alone cannot universally order operational magic. Extending our framework to the $N$-layer model motivated by the Space-Time Efficient Analog Rotation (STAR) architecture, we obtain an exact iterative update rule for the Pauli spectrum. This yields a second no-go theorem: no state-independent sequence of operations can guarantee monotonic magic improvement. Together, these theorems demonstrate that algebraic gate structures are fundamentally insufficient to dictate resource generation. To overcome this, we reframe early FTQC gate selection as a state-aware, differentiable optimization over continuous analog parameters. Finally, we identify a severe kinematic expressibility bottleneck in architectures restricted to single-qubit $Z$-rotations and show that introducing nonlinear diagonal phases, such as multi-qubit $Z$-rotation, shatters this bottleneck. This provides a fundamental principle for demonstrating early FTQC, establishing scalable magic generation as a foundational benchmark for evaluating early FTQC architectures.

We utilize the phase space analysis method to study the early evolution of the spatially closed universe and find that there exists an attractor denoting the de Sitter expansion phase, and that the universe has three distinct evolutionary paths, which correspond to the kinetic initial conditions for inflation (KICI) scenario, bouncing universe, and emergent universe. Based on the results of the phase space analysis, we calculate the primordial power spectrum and CMB TT spectrum for these models. We find that, for these models, the primordial power spectrum and CMB TT spectrum are suppressed at large scales. Moreover, the CMB TT spectra for these models overlap completely, indicating that these models are indistinguishable via their CMB TT spectra, and that the suppression and the detailed shape of the CMB TT spectrum are independent of the specific pre-inflationary dynamics or the presence of a transition stage.

Optimizing quantum circuits by reducing circuit depth is essential for improving the efficiency and scalability of quantum algorithms, particularly as quantum hardware continues to evolve. This can be achieved by restructuring quantum algorithms to allow more parallelism. A compiler is needed to automatically detect and apply these optimizations. In this work, we focus on the optimization of two fundamental quantum subroutines: GHZ state creation and CNOT/CZ chain decomposition. Traditional implementations of these subroutines suffer from linearly increasing circuit depth, which limits scalability. We propose a compiler-driven approach that automatically detects and optimizes these two fundamental quantum subroutines. Our approach reduces circuit depth through constant-depth GHZ state creation, constant depth CZ chain decomposition, and logarithmic depth recursive CNOT chain decomposition, which enhance parallel execution. Performance analysis of benchmarked algorithms shows significant reductions in depth. However, our solution also results in an increased gate count, which makes our optimization a trade-off. The gate count for the CNOT chains is doubled, where logarithmic depth reduction is achieved. The reduced circuit depth results in more efficient algorithms by reducing execution time.

In this work, we review gravitational-wave generation in a two-scalar-field cosmological model. The framework relies on a two-field scenario in which warm inflation is unified with the dark sector within a single theoretical description. It has recently been shown that this setup leads to a gravitational-wave spectrum potentially detectable by future experiments. Here we also demonstrate that the resulting spectrum is largely independent of the $φ$ field initial condition, thereby extending previous findings.

Neutral atom platforms are analogue quantum simulators that offer the possibility to map graphs onto a 2D qubit register using programmable Rubidium atoms arrays, whose valence electrons' energy state is used as qubits, using optical tweezers. This makes it possible to implement algorithms for solving graph combinatorial optimization and Quantum Machine Learning (QML) tasks, such as graph classification. However, the restrictions of real hardware, as well as the very low number of publicly available machines, make such implementation non-trivial. In this work, we manage to compute the Quantum Evolution Kernel (QEK) to extract the features from graphs of the PROTEINS dataset using the 256-qubits Aquila platform (available through AWS) and then we apply classical Machine Learning (ML) techniques for the final classification. The method is benchmarked against classical kernels, resulting in slightly better performance, proving the effectiveness of the method, even in the case of a noisy quantum simulator.

Graph embedding is a recurrent problem in quantum computing, for instance, quantum annealers need to solve a minor graph embedding in order to map a given Quadratic Unconstrained Binary Optimization (QUBO) problem onto their internal connectivity pattern. This work presents a novel approach to constrained unit disk graph embedding, which is encountered when trying to solve combinatorial optimization problems in QUBO form, using quantum hardware based on neutral Rydberg atoms. The qubits, physically represented by the atoms, are excited to the Rydberg state through laser pulses. Whenever qubits pairs are closer together than the blockade radius, entanglement can be reached, thus preventing entangled qubits to be simultaneously in the excited state. Hence, the blockade radius determines the adjacency pattern among qubits, corresponding to a unit disk configuration. Although it is straightforward to compute the adjacency pattern given the qubit coordinates, identifying a feasible unit disk arrangement that matches the desired QUBO matrix is, on the other hand, a much harder task. In the context of quantum optimization, this issue translates into the physical placement of the qubits in the 2D/3D register to match the machine's Ising-like Hamiltonian with the QUBO formulation of the optimization problems. The proposed solution exploits the power of neural networks to transform an initial embedding configuration, which does not match the quantum hardware requirements or does not account for the unit disk property, into a feasible embedding properly representing the target optimization problems. Experimental results show that this new approach overcomes in performance Gurobi solver.

Quantum low density parity check (qLDPC) codes, particularly bivariate bicycle (BB) codes, achieve competitive fault tolerance thresholds while offering substantially higher encoding rates than planar surface codes. However, their intrinsically long-range stabilizer structure makes them difficult to implement on monolithic devices with nearest neighbor connectivity and limited qubit capacity. In this work, we study the realization of a BB code in a modular multiprocessor architecture, where quantum processors are interconnected through shared Bell pairs. We consider processors with all to all internal connectivity, which is feasible on trapped ion and neutral atom platforms, enabling flexible local gate execution while inter-processor (nonlocal) gates are mediated by shared entanglement. We describe a star network architecture that can realize this distributed setting. We partition the qubits of the [[144,12,12]] BB code across 4, 6, and 12 quantum processors and analyze the resulting logical error rates and pseudo-threshold performance under circuit level noise by varying the number of processors and a scaling factor that captures the additional noise associated with nonlocal operations. We use Monte Carlo simulations with BP+OSD decoding and extend the previously known BB code ansatz to the distributed setting. Our results provide architectural insight and design considerations for distributed BB codes in modular quantum computing architectures.

Multi-controlled gates are essential primitives in quantum algorithms, yet implementing them via standard gate-level decompositions remains resource-intensive. We develop efficient pulse-level implementations of multi-controlled gates in trapped-ion systems using the Cirac-Zoller scheme. We first show that the Cirac-Zoller construction admits a freedom in the sign choice of red-sideband (RSB) pulses, which leaves the logical operation invariant up to a local Pauli-$Z$ correction. By exploiting this freedom, we construct equivalent realizations of multi-controlled gates and develop pulse cancellation for more efficient implementations of successive gates. We perform numerical simulations and show that pulse cancellation reduces the gate time and improves the state fidelity. Furthermore, we propose ancilla-free circuits for general $N$-controlled gates that use a single-controlled gate primitive and $\mathcal{O}(N)$ RSB pulses. As a key application, we apply our pulse cancellation to the linear combination of unitaries (LCU) method for block encoding. We show that the RSB-pulse cost of the select operator over $L$ unitaries can be reduced from $\mathcal{O}(L\log L)$ to $\mathcal{O}(L)$, which improves the efficiency and scalability of LCU-based quantum circuits.

Quantum Key Distribution (QKD) enables Information-Theoretically Secure (ITS) key exchange, robust even against future quantum computing threats. However, a fundamental limitation of QKD is the requirement for an authenticated classical channel, which necessitates a pre-shared secret key. In this work, we address this challenge by adopting a Hybrid Entangled Physical Unclonable Function (PUF) protocol for authentication. We demonstrate that this PUF-based method generates an ITS initial key under minimal explicit hardware assumptions. This approach allows us to experimentally perform a fully ITS-authenticated entanglement-based QKD protocol that relies solely on such assumptions, effectively eliminating the need for pre-shared secrets. This represents a significant step towards the practical realization of quantum network protocols using lightweight, readily available hardware assumptions, without weakening security guarantees.

In the standard Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime, we consider a local cosmic test mass that is boosted in some direction relative to the standard comoving observers. The geodesic (Fermi) normal coordinate system established around the world line of the boosted cosmic mass is constructed within an approximation scheme and the resulting spacetime metric is compared with the corresponding metric of the Fermi system established around the world line of a comoving observer. The circular gravitomagnetic field around the direction of motion of the boosted cosmic mass is studied.

Wormholes are a hypothetical object that connects disparate points in spacetime. It is a theoretically well-motivated black hole alternative and offers a potential observationally testable arena for probing strong-field gravity with horizon-scale images. We perform general relativistic magnetohydrodynamic (GRMHD) simulations and general relativistic radiative transfer (GRRT) calculations of accretion flows onto a Kerr-like wormhole. Adopting a Kerr black-bounce metric with a fixed throat parameter $\ell = 2.5\,\rm M$, we explore the effects of spin using both two- and three-dimensional simulations. The accretion flow is initialized as a magnetized geometrically thick torus near one mouth of the wormhole, while the opposite mouth is initially gas-free. We find that the spin parameter influences the dynamical properties on both sides of the wormhole through the frame-dragging effects. Based on the GRMHD results, we compute ray-traced images at $230\,\mathrm{GHz}$ using \texttt{RAPTOR}, and analyze the horizon-scale image structure through higher-order photon trajectories. Our GRRT calculations show that emissions originating from the immediate vicinity of the throat can dominate, in contrast to the case of a Kerr black hole. It provides the variable component of the signal and imprints a clear quasi-periodic modulation in the light curves. These properties would be useful to either confirm or rule out such exotic compact objects through horizon-scale observations.

Deep reinforcement learning (DRL), acting as a novel and powerful paradigm for quantum optimal control, offers transformative opportunities for advancing neutral-atom quantum computing. In this work, we theoretically demonstrate a DRL-based framework for realizing Rydberg controlled-NOT gates that achieve both high speed and high fidelity through the synchronous modulation of multiple pulse parameters without any prior heuristic ansatz. By introducing an incremental-update learning policy, our framework effectively regularizes the exploration of the control landscape, ensuring the generation of smooth, experimentally feasible pulse profiles while significantly reducing computational overhead compared to conventional schemes. Crucially, the framework autonomously discovers an early-cutoff policy by optimally reconciling operation speed with high-precision coherent control. Our optimized protocol achieves a peak average fidelity of 0.9991, significantly outperforming conventional methods and surpassing the critical fault-tolerant threshold. This work establishes a generalizable, AI-driven pathway for designing high-performance quantum gates and provides a robust paradigm for autonomous control field optimization across diverse qubit platforms.

We study the singlet-sector structure of mass-deformed BFSS$_{d+1}$ matrix quantum mechanics by combining the large--\(d\) Gaussian reduction with the Molien--Weyl projection. The Gaussian reduction captures the bulk matrix dynamics through a gauged harmonic oscillator, while the Molien--Weyl integral imposes the Gauss law and reorganizes the physical Hilbert space into holonomy-projected singlet excitations. We show that the very-low-temperature bosonic singlet spectrum is universally controlled by the quadratic Gram operators \(\Tr(X_aX_b)\), whose number is \(d(d+1)/2\). For \(N=2\), this result is established by explicit residue computations and character methods; for \(N>2\), it is supported by the character analysis. Thus the infrared spectrum begins as a collection of BFSS$_2$--like Gram towers, although higher invariant structures generally modify the full partition function. We also give a Hamiltonian derivation of the exceptional exact factorization at \((d,N)=(2,2)\), where the BFSS$_3$ singlet partition function equals the cube of the BFSS$_2$ one for all temperatures. This rigidity is special to the \(SU(2)\) invariant tensor structure and explains why \(d=1\) and \(N=2\) are exceptional regimes without a deconfinement crossover. Finally, we extend the Gram-counting picture to supersymmetric BFSS/BMN models and indicate how the Molien--Weyl formulation can benchmark Monte Carlo simulations in both \(X_a\)-space and holonomy space.

The Bose-Hubbard Hamiltonian can be simplified to have only two lattice sites, in which case the system being described is referred to as a dimer. Due to its structure, the hopping term of the dimer Hamiltonian enjoys invariance in a family of subspaces indexed by a whole number $k$, each subspace corresponding to a system of only $k$ particles. We have invented an inductive argument using the bosonic canonical commutation relations to find the eigenvalues and eigenvectors of the dimer hopping Hamiltonian in its $k$-particle subspaces. In particular, this Hamiltonian, when restricted to one of the $k$-particle subspaces, is exactly the spin projection operator along the $x$-axis, where the number of particles $k$ in the dimer system yields the projection matrix for spin quantum number $s=k/2$. Thus, a new method for computing the eigenvalues and eigenvectors of the $x$-axis spin projector has been unearthed. We use the explicit construction to study the dynamics of coherent states induced by the square of the dimer hopping hamiltonian. We find that it generates Schrödinger cat states in the two-site setting.

We study the deflection of light in a homogeneous plasma medium around a BTZ-ModMax black hole, focusing on the effects of the ModMax nonlinear electrodynamics parameter and the cosmological constant. Using the Gauss-Bonnet theorem applied to the corresponding optical geometry in plasma, we derive a modified expression for the deflection angle and examine how plasma dispersion alters the gravitational lensing behavior. The influence of the ModMax parameter in the presence of homogeneous plasma is compared with its vacuum counterpart, as well as with the charged and static BTZ black hole cases, revealing distinct signatures arising from nonlinear electrodynamics. This work highlights the combined impact of homogeneous plasma, spacetime curvature, and nonlinear field dynamics on light deflection in lower-dimensional black hole geometries. We further study the greybody factor and analyze how the presence of homogeneous plasma and the ModMax parameter modifies the energy emission spectrum of the black hole. Our results demonstrate that both plasma effects and nonlinear electrodynamics significantly influence the transmission probabilities and emission rates, providing deeper insight into wave propagation and observational signatures in lower-dimensional black hole geometries.

We investigate single-photon scattering in a waveguide-QED setup, where a giant molecule composed of two frequency-detuned giant atoms is coupled to two parallel waveguides via multiple connection points. The competition between coherent atom--atom coupling and the effective decay rates dictates the splitting of a single resonance into a doublet in the transmission (reflection) spectra. By tailoring the asymmetry of the decay rates and the atomic detuning, one can engineer photon-path interference to optimize the transfer between waveguides; under chiral coupling conditions, this interference can be further harnessed to realize fully deterministic routing. In the non-Markovian regime, retardation effects can reshape the spectra and actively drive transitions between the weak- and strong-coupling regimes, converting an unsplit Markovian resonance into a clearly separated doublet, or conversely merging a split doublet back into a single resonance. For sufficiently long time delays, it further generates multiple resonances and avoided crossings, enriching the spectral response. Our results demonstrate how atomic detuning, decay-rate asymmetry, and non-Markovian retardation cooperate to provide versatile, interference-based control over single-photon routing in multi-port quantum networks.

Modern lattice-based cryptography, particularly the learning with errors paradigm, relies on injecting artificial noise to secure data against quantum adversaries. This study systematically examines the theoretical and physical boundaries of this noise-reliant model across four interconnected domains: computational complexity, information-theoretic thermodynamics, quantum error correction, and quantum learning theory. Starting from the algorithmic foundation, our analysis notes that these frameworks rely on provisional complexity-theoretic assumptions that remain vulnerable to future quantum algorithmic advancements. Furthermore, by translating this cryptographic mechanism into physical thermodynamics, we illustrate that intentionally injected discrete Gaussian noise does not equate to the permanent erasure of information. Because the structural integrity of the cryptographic secret remains preserved within the ciphertext, advanced quantum error correction protocols and quantum learning models can efficiently extract the underlying mathematical kernel. Ultimately, we suggest that while lattice-based cryptography provides a robust transitional alternative, definitively classifying these frameworks as unconditionally post-quantum represents a premature classification relying on transient physical bottlenecks rather than impenetrable theoretical boundaries.

Spin priors play a fundamental role in gravitational-wave parameter estimation, yet their impact on parameterized tests of General Relativity (GR) remains insufficiently understood. In this work, we systematically investigate how spin prior choices affect the 1.5PN deviation parameter $δ\hatφ_3$ using real gravitational-wave events. We quantify prior-induced effects through the Jensen--Shannon divergence (JSD) and median shifts of posterior distributions. We find that the effective precession spin parameter $χ_p$ exhibits significantly stronger prior sensitivity than the effective inspiral spin $χ_{\rm eff}$. While $δ\hatφ_3$ is generally robust across most events, GW231123\_135430 exhibits a noticeable discrepancy, with a JSD at the $\mathcal{O}(0.4)$ level. Examining the median shift, we note that events with very short inspiral durations, such as GW231028\_153006, GW231123\_135430, and GW191109\_010717, show more pronounced shifts, indicating increased sensitivity in low-information regimes. We further explore the relationship between the prior sensitivity of spin parameters and that of $δ\hatφ_3$. No significant correlation is observed when spin parameters are inferred within the standard GR framework. However, when $δ\hatφ_3$ is included in the analysis, a strong correlation emerges between $χ_{\rm eff}$ and $δ\hatφ_3$, which we attribute to partial parameter degeneracy at the 1.5PN order. A leave-one-out test shows that the observed correlation is sensitive to the inclusion of specific events, indicating that it is partially driven by a subset of high-sensitivity events. Our results demonstrate that spin-prior choices can propagate into parameterized tests of GR in a non-trivial and model-dependent manner, and may mimic or reshape apparent deviations from GR.

Identifying causal order from restricted projective data is generally nontrivial. When two quantum players interact only through an unobserved environment, the available local measurement statistics are typically not tomographically complete, so the underlying process cannot in general be reconstructed exactly from the observed distribution. As a result, causal direction can be statistically identifiable in some cases but fundamentally indistinguishable in others. In this work, we determine necessary and sufficient conditions for deciding when an observed distribution is compatible with a memoryless sequential quantum process in a fixed direction. We show that directional conditional-independence structure and the positivity criterion based on the pseudo-density matrix, as developed in recent work by Liu, Qiu, Dahlsten, and Vedral, are not sufficient by themselves. The missing ingredient is an additional algebraic consistency requirement, and together these conditions yield a complete criterion for membership in the memoryless sequential class. We then specialize to the two-qubit Pauli setting, where the problem remains non-tomographic but becomes explicitly tractable. In this regime, we characterize when the two sequential directions are statistically indistinguishable, and we show by example that positivity alone does not exclude more general memoryful strategies, whereas the additional algebraic consistency requirement does.

Fully connected quantum networks enable scalable quantum communication, yet reliable entanglement characterization without trusting measurement devices remains challenging. Here we experimentally demonstrate measurement-device-independent (MDI) entanglement verification and quantification in a time-bin-encoded fully connected quantum network. Using a broadband periodically poled lithium niobate on insulator source combined with dense wavelength-division multiplexing, we distribute all six pairwise entangled links among four users over 20-km fiber channels, preserving high-fidelity entanglement without active stabilization of the long-distance fiber links. We show that conventional entanglement witnesses can fail under untrusted measurement conditions. By encoding trusted input states in the polarization degree of freedom of the same photons, we realize MDI measurements without ancillary photons or additional experimental resources. Both entanglement verification and quantification are obtained from the same measurement dataset. Our results establish a practical and scalable approach for reliable entanglement characterization in quantum networks.

Matrix product operators (MPOs) provide a scalable approach for quantum state tomography (QST) by offering a compact representation of many-body mixed states with limited entanglement, using only a number of parameters that scales polynomially with the system size. In this paper, we study QST for quantum density matrices that can be represented by MPOs. We first derive an equivalent characterization of Hermiticity in terms of the MPO core tensors and show that the coefficient tensor of an MPO under the Pauli or generalized Gell-Mann basis admits a real-valued low tensor-train (TT) rank structure. This establishes an explicit connection between MPO-based QST and noisy low-rank tensor completion. Motivated by this formulation, we develop an online Riemannian gradient descent (oRGD) algorithm that sequentially incorporates measurement data during the reconstruction process. With a proper initialization, we prove that oRGD converges linearly to the target MPO and succeeds with a number of distinct measurement settings that scales quadratically with the system size. As a byproduct, our analysis also yields a significantly improved sample complexity bound for the low TT rank tensor completion task. Furthermore, we propose a tailored spectral initialization method and establish its theoretical guarantee. Numerical experiments on several classes of quantum states validate the effectiveness and scalability of the proposed method.

This paper intends to realize negative refraction with absorption suppressed by the electromagneticly induced transparency(EIT) in a dense four-level atomic system. Without the two equal transition frequencies responding to the probe field, the atomic system displays a negative refraction with the simultaneously negative permittivity and negative permeability(Left-handedness). The response of the probe field is amplified and propagates transparency in some frequency extents. Therefore, our aim for searching the low-loss negative refraction can be achieved in the scheme, given the main applied limitation of the negative refractive materials is the large amount of dissipation and absorption. However, an excessive signal field intensity would increase the absorption near the resonance in our scheme.

We study the dynamics of the collapse of a nonspherical overdense patch during an early matter-dominated era and the associated production of gravitational waves (GWs) using a semirelativistic N-body framework that we develop. The collapsing patch is initialized through a Zel'dovich deformation of a homogeneous sphere and evolved in an Einstein--de Sitter background, while the emitted signal is computed directly from the numerical quadrupole evolution. We show that a reliable prediction of the signal requires a fully numerical treatment of the nonlinear collapse dynamics. In particular, fitting-based procedures and Zel'dovich-based estimates fail to capture the post-shell-crossing evolution and can over/under-estimate the emitted power of the GWs. After averaging over realizations weighted by the Doroshkevich and BBKS (peak theory) distributions, we find that the two spectra have similar shapes and remain within the same overall order of magnitude at the peak amplitude, although the BBKS result is systematically smaller. The dominant contribution arises from peaks of relatively modest height, around $ν\simeq 3$, while a larger variance significantly enhances the signal. Finally, by varying the horizon mass and reheating temperature, we map the present-day GW spectra to the sensitivity bands of different classes of detectors. In this way, the signal can populate a broad range of frequencies, from pulsar timing arrays to very high-frequency experiments, showing that GWs from nonspherical collapse can provide a probe of the pre-BBN thermal history.

Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say little about the probability itself contained in a small region. We introduce the "confidence uncertainty" $Δ^{c}x(θ_x)$ as the minimal Lebesgue measure of the support set in which the particle is found with probability at least $θ_x$, and the companion "interval confidence uncertainty" $Δ^{I}x(θ_x)$ which restricts the support to a single interval. We prove two complementary uncertainty inequalities. (i) For $θ_x+θ_p\le 1$ both confidence uncertainties can be made arbitrarily small simultaneously, so that no nontrivial product bound holds; in particular, position and momentum can be jointly localised with probability at least~$50\%$. (ii) For $θ_x+θ_p>1$ a lower bound holds: combining Lenard's projection inequality with the Donoho--Stark operator-norm bound we obtain $Δ^{c}x\,Δ^{c}p\geq 2π\hbar\bigl(\sqrt{θ_xθ_p}-\sqrt{(1-θ_x)(1-θ_p)}\bigr)^{\!2}$, and for the interval version we obtain the sharp implicit Landau--Pollak bound $Δ^{I}x\,Δ^{I}p\geq 4\hbar\,λ_{0}^{-1}\!\bigl((\sqrt{θ_xθ_p}-\sqrt{(1-θ_x)(1-θ_p)})^{2}\bigr)$, where $λ_{0}(c)$ is the largest prolate-spheroidal eigenvalue. We support the analytical bounds with numerical evaluation of $λ_{0}(c)$, provide closed-form small-$c$ and large-$c$ asymptotics, compute the optimal Slepian-superposition states that saturate the interval bound, and compare the resulting product against the variance Heisenberg--Kennard, the Białynicki-Birula--Mycielski entropic, and the Donoho--Stark concentration bounds.

Periodically driven systems provide a powerful platform for quantum multiparameter estimation. Constructing a static effective Hamiltonian in a proper rotating frame is commonly employed to assess the attainable precision. However, such an approach becomes nonfeasible for more general time-periodically driven systems. To tackle this dilemma, we develop a quantum multiparameter estimation strategy in the Floquet theory framework. The contributions of Floquet eigenmodes, quasienergies, and multi-photon processes to the quantum Fisher information matrix and measurement incompatibility are determined, respectively. Moreover, this approach is applied to a ring-shaped Rashba spin-orbit interferometer model exhibiting the topological phase transition (TPT). In the vicinity of the TPT boundary, we reveal a pronounced enhancement in the estimation precision of multiple parameters with the Heisenberg limit scaling and even higher. Meanwhile, the measurement incompatibility vanishes in an oscillatory manner, and the stroboscopic projective measurement enables the highest estimation precision achievable. This work provides a complete Floquet picture for time-dependent critical quantum multiparameter estimation.

Fault-tolerant quantum computation (FTQC) critically depends on real-time classical decoding, which is rapidly emerging as a system bottleneck. As quantum systems scale, decoding latency and throughput limitations lead to exponential syndrome backlogs and logical operation stalls. While hardware accelerators and parallel windowing offer pathways to speed up decoding, dynamically deploying a finite pool of decoders across a vast quantum error correction architecture remains an unresolved resource allocation problem. To address this, we formulate FTQC decoding as a constrained dynamic scheduling problem by utilizing a spatio-temporal framework based on slices. We propose Triage, a dual-mode architecture that mitigates operation stalls by adaptively combining a cost-efficient heuristic scheduler with a priority-aware emergency mode to rapidly resolve the causal cone of critical operations. Our evaluation shows that Triage maintains low algorithm stalls and logical error rates even under scarce classical resource constraints. Across various benchmarks, Triage achieves an average logical error rate reduction of 52.6% compared to standard temporal parallelism, enabling an efficient classical control plane for scalable FTQC architectures.

We derive the unitary dynamics of a four-qubit isotropic Heisenberg XXX chain with tunable next-nearest-neighbor coupling $α$, initialized in a Bell-type product state. Closed-form expressions are obtained for the state fidelity $F(ρ(0),ρ(t))$, the $l_1$-norm coherence $C_{l_1}(ρ(t))$, and the entanglement of formation $E_F^{12}(t)$ and $E_F^{34}(t)$ for the two-qubit subsystems (12) and (34). All quantities depend exclusively on the composite phase $φ= (α+1)t$. Fidelity obeys $F = |\cos(φ/2)|$ and remains frozen at $F \equiv 1$ for $α= -1$. Coherence follows $C_{l_1} = \sin^2(φ/2)$, vanishing identically at $α= -1$ and exhibiting sensitivity proportional to $|α+1|$. The entanglement of formation is an entropic function of $φ$, displaying banded oscillations and freezing at $α= -1$. The phase $φ$ unifies all observables, linking the rate of resource variation to $|α+1|$ and identifying maximal sensitivity along $(α+1)t = π/4 + kπ/2$. This framework provides exact benchmarks for few-qubit quantum devices and a controlled pathway for extensions to noise, finite temperature, and larger systems.

We introduce a new family of cosmological attractors with non-minimal coupling of gravity and non-canonical kinetic terms. In the Einstein frame, these models transform into a class of exponential and polynomial attractors with the spectral index $n_{s}$ spanning a broad range $1-2/N \leq n_{s} < 1-1/N$, and $r$ can decrease to zero in the limit $ξ\to \infty$. This is sufficient to match any combination of Planck, BICEP/Keck, ACT, SPT, and DESI data. We present a supergravity implementation of these models.

This paper studies uniform mixing in continuous-time quantum walks. We show that for some unitary signing $σ$ the complete graph $K^σ_n$ has probabilistic uniform mixing. In contrast, it is known {\em no} complete graph has uniform mixing except for $K_2$, $K_3$, and $K_4$. Our technique is based on a stopping rule for quantum walks which reduces global to local uniform mixing. As a special case, we found an orientation of $H(n,4)$ that mixes to uniform faster than any other Hamming graphs. We also show that there are infinite families of oriented circulants with {\em average} uniform mixing. This is a chiral violation of Godsil's {\em No-Go} theorem which states that no graph has average uniform mixing except for $K_2$.

Dynamic quantum circuits integrate mid-circuit measurements and feed-forward operations to enable real-time classical processing and conditional quantum logic. These capabilities are central to key quantum protocols such as quantum error correction, and have recently demonstrated significant potential for reducing quantum resources, including circuit depth and gate count, across a range of applications. However, executing dynamic circuits on real quantum hardware introduces a critical trade-off: while resource requirements decrease, circuit fidelity degrades due to high error rates of mid-circuit measurements, as well as the decoherence errors accumulated during the extended idle periods introduced by both mid-circuit measurements and feed-forward operations. In this paper, we systematically investigate the impact of standard error mitigation techniques on dynamic circuit applications pertaining to Hamiltonian simulation and ground state estimation of physically relevant systems like the Heisenberg model. We explore dynamical decoupling (DD) as a strategy to suppress decoherence and crosstalk errors during idle windows introduced by mid-circuit measurements and feed-forward delays, and also examine error mitigation via zero-noise extrapolation (ZNE). Through experiments conducted on IBM quantum hardware, we benchmark effective combinations of these strategies that maximize the practical benefits of dynamic quantum circuits in these applications. We demonstrate that a combination of DD and ZNE is effective in mitigating the errors introduced during mid-circuit measurements and feed-forward operations, as well as the errors arising from faulty measurements. This approach yields a fidelity improvement of at least 60% in ground state estimation and reduces observed error of time-evolved states by up to 99% for the Ising model and up to 20% for the Heisenberg model.

Ferroelectric materials have colossal optical nonlinearities, but their integration into quantum photonic chips is made challenging by the additional loss mechanisms that they introduce. Here we present a perturbative theory that expresses non-absorptive (elastic) photon scattering-induced loss as a functional of a general spectral density for spatial fluctuations of electric permittivity. We apply the theory to calculations of attenuation coefficients $α$ in slab waveguides in order to compare two distinct loss mechanisms: Interface roughness and ferroelectric domain disorder. our theory can account for realistic roughness without special symmetry considerations, and it demonstrates how to use electron microscoopy images of ferroelectric domains to obtain explicit numerical predictions for $α$. Loss is maximum when the mean domain length is comparable to the wavelength of light (Mie regime), indicating that, for telecom wavelengths, sub-micron domains (Rayleigh regime) or single domain waveguides provide equivalent strategies for reducing loss.

For an infalling circular string, we study particle production, Krylov complexity, Lanczos coefficients, and operator growth induced by quantum fluctuations. Using canonical quantization in the squeezed state formalism, we show that significant particle production arises only in the radial sector as the string approaches the black hole horizon, while angular modes remain weakly excited. Exploiting the equivalence between particle number and Krylov complexity for two mode states, we find that nontrivial complexity scaling emerges only in the near-horizon, effectively thermalized regime, where the state approaches a thermofield double form. In this limit, the particle number exhibits a polynomial dependence on the initial position of the probe string. We further identify a linear dependence of the operator growth rate on the initial position of the probe string, suggesting a universal scaling behavior of operator growth and providing support for the complexity volume correspondence.

We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens of group theory, we expose the possibility that physical systems such as molecular orbitals, condensed phase assemblies and optical beams may be designed such that these contain information pertaining to the solution to hard mathematical problems such as prime-factoring. We discuss real molecular systems, whose orbitals are constructed from symmetry-adapted linear combinations of atomic orbitals, and show that these contain information pertaining to the prime-factors of corresponding integers. Due to the broad significance of prime-factoring towards a variety of encryption problems in cyber-security, we believe this novel and fundamental approach may have broad impact.

Certifying quantum behavior from classically accessible data is essential for secure communication and scalable quantum technologies. While powerful certification methods such as Bell nonlocality and quantum steering exist, their implementation typically requires entanglement or additional assumptions, and experimental demonstrations mainly focus on low-dimensional systems. In minimal prepare-and-measure scenarios, where a sender encodes information into quantum states and a receiver performs a single measurement, robust certification becomes particularly challenging, especially in the presence of noise and in higher-dimensional Hilbert spaces. Here, we propose, design, and experimentally implement a protocol that certifies quantumness between two distant parties without the need for preshared resources or measurement incompatibility. The experiments are carried out using the orbital angular momentum degrees of freedom of single photons, chosen for providing increased dimensionality that is scalable. We demonstrate the robustness of the protocol through rank-stability analysis of the observed correlations, which enables the certification of non-classicality even in the presence of noise. Our results provide a practical route to validate high-dimensional quantum communication systems and open new possibilities for secure and dimension-efficient quantum information processing.

While it has been widely recognized that genuine quantum advantage for practical problems might only be achieved with fault-tolerant quantum computers, it is still not entirely clear whether the required quantum error correction will be physically feasible. In the present work, we carefully analyze the required energy resources to encode the logical qubit states for repetition, perfect, and Steane codes. We find that there is a universal trade-off between the target precision and the required energetic resources. Importantly, we find that the energetic resources intimately depend on the specific physical realization of a quantum error correction code, and that the required resources scale exponentially with the targeted precision of the encoding.

Optically addressable spin defects in silicon carbide, including the neutral divacancy (VV$^0$) and the negative nitrogen-vacancy (NV$^-$), are among leading building blocks of solid-state quantum technologies. Integrating these defects into photonic structures such as nanopillars improves photon collection efficiency, but the consequences extend further. We show that the sub-wavelength geometry of nanopillars drastically modifies the local electromagnetic environment, providing optical access to defect transitions that are otherwise suppressed by selection rules in bulk material. Using low-temperature photoluminescence spectroscopy, we observe that emission from the PL3 divacancy, which is nearly absent in planar devices, becomes pronounced in nanopillars owing to a polarization transformation of the excitation field within the pillar. We further leverage the orientation-dependent collection of nanopillars to resolve the origin of previously ambiguous spectral lines. In particular, the NV4$'$ feature displays the signal enhancement expected for axially oriented NV$^-$ centres, consistent with assignment to a higher excited state of the $kh$ defect configuration. Our results establish nanophotonic integration as a symmetry-sensitive probe that can both activate nominally dark transitions and identify the dipole character of poorly understood defect states.

We study compression strategies for multipartite entanglement distribution under uncertainty in the partitioning of the quantum state. When the partition is not known at the time of state preparation, we show that a joint design of the resource state and a family of compression schemes can increase the entanglement across partitions under a fixed transmission budget. We formulate this as a source coding problem and derive non-asymptotic upper and lower bounds on the achievable average entanglement subject to an average coding rate. We furthermore design an efficient method for jointly optimizing states and lossless compression maps by exploiting the inherent symmetry of weighted Dicke states. In the bipartite case, we propose practical constructions that closely approach the derived upper bound, and more generally we provide practical constructions for multipartite settings.

The study of hyperbolic binary black hole encounters yields an effective probe of the strong field regime of black holes, thus providing an additional channel to test General Relativity. We study the scattering of two black holes in Einstein-scalar-Gauss-Bonnet gravity, a well-motivated effective field theory of gravity, by comparing the scattering angle obtained from the first fully nonlinear black hole scattering simulations with its effective-one-body analytic description. We obtain excellent agreement between analytics and numerics, exhibiting accurate capturing of strong-field scalar-gravitational dynamics. Our work paves the way towards semi-analytical waveform templates of compact object binaries in modified theories of gravity.

We analyze the emergence of nonlocal magic in Schwinger pair creation in strong non-Abelian (chromo)electric fields using holography. The produced quark--antiquark pair is entangled into a color singlet, yet accelerates into causally disconnected Rindler wedges. Using the Casini--Huerta--Myers conformal mapping and the probe-brane framework, we compute the refined Rényi entropy and its derivative, which captures the antiflatness of the entanglement spectrum for a spherical bipartition. We find that for boundary spacetime dimension $d>2$, the entanglement spectrum is non-flat, implying the dynamical generation of nonlocal magic in the pair creation process. Interestingly, the nonlocal magic in the holographic dual can be obtained from the free energy of the probe action.

Quantum metrology holds the potential to enhance magnetic field sensing beyond current limits. However, in the presence of realistic noise, this advantage degrades to the Standard Quantum Limit. While recent algorithmic and variational techniques attempt to recover this scaling, they are hindered by stringent control requirements on the probe state that are infeasible in the near term, or by barren plateaus and interpretability issues inherent to black-box variational quantum circuits. Here, we introduce Variational Inference and Sensing with Twin Ansätze (VISTA), a closed-loop protocol that combines passive sensing, or where the probe state is left to evolve without any active control, with physics-informed variational optimization. In the VISTA framework, a probe state evolves under a Lindbladian master-equation, and is compared, via the Swap test, to a parameterized ``quantum twin", a shallow quantum circuit designed to mimic the underlying pure-state or Lindbladian master-equation dynamics. By restricting the optimization space to the physical parameters of interest, VISTA circumvents barren plateaus. We demonstrate that by coupling the protocol with a classical optimizer and high shot counts, VISTA can temporarily achieve near-Heisenberg scaling for moderately noisy qubits over a finite range of system sizes. Furthermore, we introduce a Quasi-Normalization technique that sharpens the loss gradients, enabling simultaneous extraction of both the coherent signal $θ$ and the environmental noise rate $γ$ with low absolute error. Finally, we extend VISTA to the multi-parameter vector metrology regime, enabling simultaneous parameter extraction from a transverse-magnetic-field Hamiltonian. By eliminating the need for complex, open-loop control and processing, VISTA offers a highly practical, resource-efficient framework for near- to intermediate-term quantum sensors.

Variational quantum eigensolver ansätze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis captures the electronic correlation of the system. Computing optimized orbital coefficients via classical routines is computationally expensive and must be performed independently for each molecular geometry -- a bottleneck that limits scalability across chemical space. We present a graph neural network framework that predicts optimized orbital coefficients directly from molecular geometry and pair-wise bonding structure. Trained on hydrogenic systems of modest size ($H_4$ and $H_6$) across tens of thousands of geometries, our model transfers to larger, unseen systems ($H_8$, $H_{10}$ and $H_{12}$) without retraining -- demonstrating strong out-of-distribution generalization with respect to system size. When evaluating on structured and random configurations, and comparing against energies obtained with full classical optimization, our model reaches mean absolute energy errors $\mathcal{O}(10^2)$ and $\mathcal{O}(10)$ milli-Hartrees, respectively. Beyond energy estimation, the predicted orbitals serve as high-quality warm-start initializations that substantially reduce optimizer iterations to ground-state energy convergence. These results establish graph neural networks as an effective and scalable strategy for accelerating orbital optimization in hybrid quantum-classical workflows, directly reducing the classical pre-processing overhead that currently limits the practical deployment of variational quantum eigensolver on near-term quantum hardware.

Integrated quantum photonics has emerged as one of the leading platforms for scaling quantum information processing, offering compact, stable, and low-loss hardware with precise phase and mode control. Advances in integrated photonics architectures and active programmability now enable complex, high-dimensional transformations essential for quantum advantage tasks. We introduce an integrated, reconfigurable 3D photonic device with 128 modes for manipulation of single-photon quantum states (Qolossus 3D). Leveraging a continuously coupled architecture and thermo-optic programmability, the platform implements reconfigurable unitary transformations at unprecedented scale for integrated quantum optics. Exploiting indistinguishable single photons demultiplexed from a quantum dot source, we perform Boson Sampling across the large-dimensional chip and analyse the resulting output distributions for up to 4 photons. We then exploit it to demonstrate randomness generation via Boson Sampling. Agreement with theoretical predictions validates both the device's reconfigurable operation and the generation of random numbers. Our results highlight the scalability, stability, and precise control of integrated photonics for quantum information processing.

We investigate the role of quantum state texture in dynamical quantum phase transitions by establishing a direct connection between critical nonequilibrium dynamics and the recently introduced notion of rugosity, a measure of the quantum state texture. Considering a generic quench protocol, we analyze both standard formulations of the dynamical quantum phase transition. For type-I transitions, defined through the long-time behavior of an order parameter, we show that the time averaged rugosity, evaluated in the eigenbasis of the pre-quench Hamiltonian, acts itself as an order parameter, sharply distinguishing the dynamical phases. In the Lipkin-Meshkov-Glick model, this behavior is traced back to the underlying semiclassical structure, where the crossing of the excited-state quantum phase transition separatrix controls the redistribution of the state over the pre-quench energy basis. For type-II transitions, characterized by nonanalyticities in the Loschmidt rate function, we demonstrate that rugosity acquires a universal interpretation. For a suitable choice of basis, the rate function is exactly given by the density of rugosity, establishing a model-independent equivalence. Moreover, we show that even in physically motivated bases, such as the pre-quench energy eigenbasis, rugosity provides clear signatures of dynamical criticality. Our results place rugosity within a broader class of quantities diagnosing dynamical quantum phase transitions, including complexity and entropy production, while highlighting its distinct role as a measure of a basis-dependent quantum resource. This work provides an information-theoretic perspective on dynamical critical phenomena and opens new directions for exploring quantum texture in nonequilibrium many-body systems.

Understanding mixed-state quantum phases is a central challenge in the era of quantum simulation, where many existing studies focus on renormalization fixed points. In this work, we move beyond the renormalization fixed-point paradigm by constructing a quantum phase transition connecting two distinct one-dimensional fixed points, both exhibiting finite conditional mutual information and one of which is intrinsically nontrivial. We analytically establish phase equivalence within each of the two phases by explicitly constructing low-depth, quasi-local channel circuits that connect states within each phase. Crucially, our approach leverages the parent Lindbladian construction to generate the desired channel circuits. We further demonstrate that this framework generalizes naturally to a broad class of intrinsically nontrivial mixed-state quantum phases. Our method establishes a framework for rigorously analyzing phase equivalence of intrinsically non-trivial mixed states beyond the renormalization fixed points.

The main aim of the present work is to demonstrate that the analogue gravity phenomena is not an artifact of linear perturbation, rather gravity-like effects emerge through the non linear higher order perturbation of transonic fluid as well. To establish that fact, a spherically accreting astrophysical system has been considered where the hydrodynamic accretion with a relativistic, multi-component equation of state with position dependent adiabatic index onto compact astrophysical objects has been considered. rate. By extending the acoustic metric formalism beyond the linear regime, it has been shown that the aforementioned perturbations satisfy a covariant wave equation in an effective acoustic spacetime with non-linear corrections, making the analogue geometry dynamical. As a consequence, the acoustic horizon can shift (inward or outward), depending on the relative amplitudes of density, temperature, and mass accretion-rate fluctuations. This provides a more realistic framework to investigate the dynamics of the non-linear analogue spacetime in astrophysically relevant accretion flows.

The present work addresses an axisymmetrically accreting black hole system from three perspectives: the astrophysical, the dynamical systems, and the emergent gravity standpoint. Steady-state equations governing low angular momentum axially symmetric accretion under a pseudo-Kerr potential are formulated for a multi-species flow with a spatially varying adiabatic index. The resulting transonic solutions are shown to be multi-transonic and may accommodate a stationary shock. Critical points are classified via perturbative dynamical systems methods, and linear stability analysis confirms that the stationary solutions remain stable under radial perturbation. The ensuing acoustic geometry harbours acoustic black holes at the sonic points and an acoustic white hole at the shock location, whose causal structure is constructed via the Carter--Penrose diagram. The surface gravity associated with each acoustic horizon is computed using a generalized expression that accounts for the spatial variation of the local sound speed.

Determining the active screening mechanism from a general scalar-tensor Lagrangian remains a challenging problem. As a diagnostic tool, we present a systematic study of nonlinear cosmological perturbations in luminal Horndeski theories. Working in the $α$-basis on a flat FLRW background, we derive and organise the full set of unapproximated second-order perturbation equations, and systematically apply the quasi-static and weak-field limits. We find that second-order effects modify only the scalar field equation. We derive, for static and spherically symmetric configurations, a master screening equation recovering the Vainshtein and Chameleon mechanisms. We also identify a novel regime, which we term Phaedrus screening, characterised by a screening radius that scales linearly with the source mass. For each mechanism, we derive analytical and numerical solutions and clarify the conditions under which they activate. Finally, we introduce two new publicly available software packages: (i) xAlpha, a Mathematica package to compute and organise perturbation equations in scalar-tensor theories, and (ii) escut, a Python module to solve the nonlinear scalar equation. In many cases, these tools enable the identification of the active screening type directly from a luminal Horndeski Lagrangian.

For a many-body system in equilibrium, described by a thermodynamically stable Hamiltonian, quantum criticality is associated with structural changes of the many-body ground state. However, there exist physically relevant models, notably, certain quadratic bosonic Hamiltonians (QBHs), which fail to have a ground state. QBHs can be dynamically stable or unstable. We show the notion of criticality is meaningful for the entire class of QBHs that are dynamically stable or at the boundary of instability, regardless of thermodynamic stability, and that the key state for such QBHs is a naturally and unambiguously defined quasiparticle vacuum (QPV). This state is Gaussian, and coincides with the ground state if the QBH is thermodynamically stable. We identify a relevant spectral gap, the Krein gap, associated to the minimal spectral separation between creation and annihilation operators, and show that the QPV is unique when the Krein gap is positive. We prove that, for dynamically stable QBHs with finite-range couplings, correlations are exponentially bounded unless the Krein gap closes, which is associated with one of two spectral degeneracies: an exceptional point or a Krein collision. Consequently, long-range QPV correlations can ensue. Thus, the Krein gap takes the role of the spectral gap for dynamically stable QBHs, and the boundary of dynamical stability and criticality (associated to exceptional points) or multicriticality (associated to Krein collisions) are the same. We also find that bosonic critical behavior beyond thermodynamic stability is witnessed by the scaling of the entanglement entropy and other indicators of equilibrium criticality from information geometry. Our framework opens the door to investigating all dynamically stable QBHs through the lens of critical phenomena, including thermodynamically unstable ones from photonics, cavity-QED, and magnonics.

High-rate bivariate bicycle (BB) codes are promising low-overhead quantum memories, but their stabilizer checks typically have weight $6$ or higher, making syndrome extraction challenging. We introduce subsystem bivariate bicycle (SBB) codes, a translation-invariant CSS subsystem construction that realizes BB-code logical structure using local weight-$4$ gauge measurements. Their stabilizer syndromes are inferred by multiplying the corresponding gauge outcomes. We further show that nonlocal stabilizers in translation-invariant CSS subsystem codes can be detected using a determinantal-ideal criterion based on the gauge-operator commutation matrix. When this criterion excludes nonlocal stabilizers, a finite-depth Clifford circuit decouples gauge qubits and identifies the protected subsystem with a corresponding BB stabilizer code. An SBB code is topological, meaning that it has no nontrivial local logical operators, if and only if the corresponding BB code is topological. A finite search yields low-overhead examples including $[[27,6,3]]$, $[[75,10,5]]$, and $[[108,12,6]]$; the latter encodes six times more logical qubits than a subsystem surface code at the same block length and distance. These results show how gauge degrees of freedom can make high-rate BB logical structure compatible with local weight-$4$ syndrome extraction.

We develop a formulation of perturbation theory on spherically symmetric backgrounds based on self-dual curvature equations combined with spherical harmonic expansions. The resulting framework unifies the Regge-Wheeler-Zerilli (RWZ) and Bardeen-Press-Teukolsky (BPT) formalisms and is designed to combine key advantages of both. The use of self-dual variables is crucial, and makes quasinormal mode isospectrality manifest, when present. We present the formalism first for a general energy-momentum tensor, and then specialize to vacuum General Relativity with matter sources to illustrate its practical advantages. A central result is that the RWZ and BPT equations arise directly as different components of a single tensorial curvature equation. We also show that, in the frequency domain, the metric can be reconstructed algebraically from any of the proposed master functions and their derivatives, and we comment on possible obstructions to such a reconstruction in the time domain. A Mathematica notebook, based on xAct, that implements the formalism and was used in our computations is released alongside this work.

We analyse three-dimensional Einstein gravity coupled to a massive complex scalar field with double-trace boundary conditions. Using high-precision spectral methods, we construct regular AdS$_3$ boson stars together with axisymmetric and non-axisymmetric hairy black holes. For each azimuthal number $m$, the hairy black holes bifurcate from the BTZ family at the corresponding double-trace instability onset. When the double-trace parameter satisfies $κ< κ_{\rm AdS}$, global AdS$_3$ becomes unstable and we identify its nonlinear endpoint as a zero-frequency boson star with energy below that of AdS$_3$, thereby providing the true ground state of the theory. In the microcanonical ensemble, hairy black holes always carry greater entropy than BTZ at fixed mass and angular momentum, and thus dominate whenever they exist. With notable exceptions, typically hairy black holes do not dominate the canonical nor the grand-canonical ensembles. We further show that, in the singular extremal limit, axisymmetric black holes saturate a generalised minimum-energy theorem under double-trace boundary conditions. These results yield the full nonlinear phase diagram of AdS$_3$ gravity with double-trace deformations.

Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the corresponding bound for estimating a function of multiple parameters-each coupled to distinct and possibly non-commuting generators-remains unknown in general. Here, we derive the ultimate quantum limit and present an estimation protocol for any function of parameters in a general Hamiltonian that attains this bound. We show that, although the task is fundamentally a multiparameter problem, our tight bound reduces to an optimized single-parameter quantum Cramér-Rao bound, even for arbitrary generator sets. Our result unifies and extends previous works, providing a general framework for optimal function estimation in quantum systems.

We study the decay of general initial states out of a metastable potential well in quantum mechanics. We provide a closed-form expression for the probability current that tunnels through the barrier in terms of the resonant states into which the initial state can be decomposed. All ingredients in the equation are computed analytically to first subleading order in the semiclassical limit. Specializing to a coherently-oscillating initial state, we derive an approximation to the time-dependent decay rate and demonstrate its accuracy by comparing it to a numerical solution of the Schrödinger equation.

Fault-tolerant quantum computing requires understanding how error-correcting codes perform on diverse physical hardware. This is typically assessed via noisy stabilizer simulation of logical circuits at HPC scale, combined with a noise model that yields a logical error rate for the relevant code distances and depths. The uniform depolarizing model is the standard baseline, but its homogeneous assumptions fail to capture the heterogeneity, asymmetries, and correlations of real devices, where Pauli, measurement, and spatio-temporal errors are not weakly coupled. Yet these same structured features create opportunities for joint code-hardware co-design, motivating noise models that more faithfully reflect target hardware while remaining tractable to simulate. We introduce FTPrimitiveBench, a systematic benchmarking approach for studying how logical primitives interact with hardware-motivated noise. It supports both custom specifications and representative structured noise families: Pauli bias, measurement bias, and spatial or spatio-temporal non-uniformity -- together with generators for core surface-code Clifford primitives: logical memory, lattice surgery, transversal logical Hadamard, and the logical phase gate via lattice surgery. We find that structured noise affects these primitives in qualitatively distinct ways, with outcomes shaped by the interplay between noise model, primitive, and decoder choice. These results extend memory benchmarks to active logical computation, where the interaction between noise structure and primitive implementation matters. By standardizing the link between noise-model specification and primitive construction, FTPrimitiveBench enables reproducible comparative studies of QEC protocols and decoders, supporting hardware-aware co-design of fault-tolerant architectures. Code: https://github.com/ShuwenKan/FTPrimitiveBench.

This study investigates the performance and ergotropy protection of open collective quantum batteries subject to superradiant decay. By employing a passive spectral detuning strategy within an intermediate cavity, an optimal detuning value ($Δ^*$) is analytically derived and numerically verified to spectrally isolate the system and protect quantum coherence, achieving up to 1088% ergotropy improvement for single qubits and superextensive collective advantage for $N \ge 3$. Our analysis resolves a "non-Markovian paradox," revealing that maximizing ergotropy does not strictly require non-Markovian memory; rather, suppressing environmental memory via detuning optimally preserves coherence, which serves as the fundamental resource. Survival maps across different environments demonstrate that thermal noise dissipates coherence more severely than telegraph noise. Finally, we establish that collective amplification of the effective coupling ($g_{\rm eff} = g\sqrt{N})$ inevitably drives large qubit arrays into the ultra-strong coupling regime, providing a quantitative ceiling $N_{\rm max}$ on the validity of the Tavis-Cummings description and the current ergotropy protection protocol.

The observational validation of General Relativity (GR) has been propelled in recent years by recent breakthroughs in Very Long Baseline Interferometry (VLBI) augmented by ALMA. We explore ALMA2040 opportunities to transform these studies through greatly improved sensitivity and a multi-frequency approach. The focus will be on placing most stringent constraints on GR and alternative theories in the strong-gravity regime, and on understanding the formation and launching of relativistic jets.

We investigate a cosmological model based on a massless nonlinear spinor field coupled to a Modified Chaplygin Gas (MCG) in the Kantowski--Sachs spacetime, aiming to probe anisotropies and unified dark sector dynamics. The model parameters are constrained using recent observational data, including Pantheon+, cosmic chronometers, DESI DR2, and CMB distance priors, via a Markov Chain Monte Carlo analysis. We find $H_0 \sim 67$--$68~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, while the shear parameter is consistent with zero, indicating an effectively isotropic Universe at late times. The model reproduces late-time cosmic acceleration with a present-day deceleration parameter $q_0 \sim -0.49$, and provides a good fit to the data, yielding a lower minimum $χ^2$ than $Λ$CDM, and is favored by the Akaike Information Criterion. Overall, the spinor field MCG model in Kantowski--Sachs spacetime offers a viable framework that naturally incorporates anisotropy and a unified description of dark matter and dark energy, consistent with current observations.

The late-time acceleration of the universe remains one of the most significant open problems in modern cosmology. Modified gravity frameworks such as $f(T)$ gravity provide a geometric alternative to dark energy by attributing cosmic acceleration to torsional effects. In this study, we present a comparative analysis of three different forms of $f(T)$ models: (i) a simple power-law form $f(T) = η(-T)^{n}$, (ii) the exponential form $f(T) = βT_{0}\left(1-e^{-p \sqrt{T/T_{0}}}\right)$ and (iii) a logarithmic form $f(T) = γT \ln\!\left(\frac{T}{T_{0}}\right)$. Using parameterization of the deceleration parameter $q(z)$ and the corresponding $H(z)$ expression, we constrain the model parameters with the recent Hubble parameter and BAO data through a Markov Chain Monte Carlo (MCMC) approach. The physical behavior of the effective energy density, equation of state parameter, squared sound speed, cosmological $Om(z)$ diagnostics, and energy conditions (NEC, DEC, SEC) were investigated for all three models. Our comparative analysis shows that all models asymptotically approach the $Λ$CDM behavior at late times, while they differ in stability properties and energy condition behaviors. In particular, the violation of the strong energy condition (SEC) has emerged as a common feature consistent with current accelerated expansion. This study highlights how different $f(T)$ functional forms can yield distinct cosmological dynamics while maintaining consistency with observational data.

Coarse-grained descriptions can be used to account for physical processes in which information is lost or not entirely accessible. In this paper, we start by proposing a connection between effective, coarse-grained descriptions of quantum dynamics and the quantum conditional states formalism. In doing so, we address necessary and sufficient conditions for the existence of emergent dynamics from a subjective Bayesian point of view. Although our solution is (quasi-)optimal, the dynamics it determines are shown to be analytically limited -- it solves the problem in a state-by-state case. Due to this limitation, we then implement semidefinite programming techniques to investigate the existence of effective dynamics in four paradigmatic scenarios. The existence of such an effective dynamics motivates the introduction of a new robustness measure that quantifies how much noise can be added to a microscopic dynamics without compromising its compatibility with a given coarse-grained description. Finally, we also show how one can analytically determine a valid emergent description in several examples.

The Earth--Moon binary is a resonant detector for stochastic gravitational-wave background (SGWB) at harmonics of the lunar orbital frequency. We quantify high-power amplitude-modulated continuous-wave lunar laser ranging (AM-CW LLR) as a $μ$Hz SGWB probe. The dominant low-eccentricity response is at $f_2=2/P_{\rm M}=0.847245\,μ{\rm Hz}$. AM-CW LLR measures radio-frequency phase on a GHz-modulated 1064 nm optical carrier reflected by lunar corner cubes, giving range and range rate observables. With an $80\,μ{\rm m}$ absolute range uncertainty, a 5-year campaign with statistically independent AM-CW phase-normal-point rate of $ν_{\rm eff}=500\,{\rm yr}^{-1}$ has response-calibrated sensitivity $Ω_{\rm gw}^{95}=5.29\times10^{-9}D_{\rm cov}$; a mature implementation with $σ_R=50\,μ{\rm m}$ gives $2.07\times10^{-9}D_{\rm cov}$, where $D_{\rm cov}\ge1$ is a covariance-degradation factor for time-correlated residuals and nuisance-parameter correlations in the global solution. Anticipated first-order phase-transition and compact-binary signals lie above the nominal 5-$σ$ covariance-amplitude threshold for $D_{\rm cov}\lesssim3.6$ and $5.4$, respectively, in the $80\,μ{\rm m}$ case, and for $D_{\rm cov}\lesssim9.1$ and $13.7$ in the $50\,μ{\rm m}$ case. Thus the experiment is a sharp covariance test: absolute range carries the SGWB signal, while range rate and multi-reflector differential data determine whether nuisance correlations keep $D_{\rm cov}$ below the discovery margins.

We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting continuous-time dynamics is an integro-differential equation that augments the Gorini-Kossakowski-Sudarshan-Lindblad equation with a memory integral, and is capable of describing the quantum state of systems exposed to noise with any integrable power spectral density with no further approximations. We then establish a formalism to evaluate multi-time correlations of measurement outcomes in this general setting, obviating the need for a regression theorem. As an application, we derive the emission spectrum of a driven two-level system coupled to a non-Markovian bath: the familiar Mollow triplet acquires a frequency-dependent linewidth that encodes the memory of the bath. Our work provides a rigorous yet transparent description of the quantum state of non-Markovian systems, opening the door for state estimation and state-based quantum control beyond the Markovian regime.

By confining a Bose-Einstein condensate in a vertical lattice subjected to a gravitational potential, we analyze the quantum Fisher information to determine its scaling with respect to time, system size and particle number. Our results reveal that in the localized phase, on-site interactions $U$ amplify the quantum Fisher information by a factor with respect to resonance condition $U=mh$ where $U$ is factor of gradient field amplitude $h$. This precision enhancement can be employed in gravitational acceleration measurements with a finite number of particles trapped in optical lattices.

Sample-based quantum diagonalization (SQD) constructs subspaces from computational-basis configurations obtained via measurements of a quantum state, with the goal of approximating low-energy eigenspaces of many-body Hamiltonians. The effectiveness of this approach relies on the assumption that physically relevant states admit a compact representation in the computational basis. We investigate this assumption by analyzing SQD subspaces constructed directly from configurations of exact ground states of Heisenberg and Hubbard model lattices. By eliminating state-preparation and measurement inefficiencies, we isolate the intrinsic configuration-space structure of the wavefunction. We determine the minimal number of configurations required to reproduce the ground-state energy within fixed accuracy thresholds and find that this number grows exponentially with the system size. Notably, this scaling persists even under optimal inclusion of configurations in order of decreasing probability, demonstrating that it originates from intrinsic delocalization of the wavefunction rather than sampling inefficiencies. Our results indicate that SQD effectively probes the configuration-space entropy but faces fundamental scalability limitations for these models.

Magic-square constraints define Diophantine systems whose solutions, in several natural families, exhibit rigid periodic structure. We study this structure in an oracle setting, where a marked set of integers is given by black-box access and the goal is to decide whether it encodes a magic square. For $3\times 3$ magic squares and weighted variants, we prove explicit periodic characterizations that reduce detection to period finding. For larger orders, we identify a class of solutions built from repeated arithmetic patterns, which can be detected via the quantum Fourier transform. We then introduce a shifted-oracle method, based on interference between an oracle and its translates, that helps reconstruct solutions in structured cases. Together, these ingredients give a quantum framework for detecting and reconstructing certain magic-square solutions under suitable assumptions. We also derive finite bounds that make some instances exhaustively solvable and obtain Shor-based criteria for certifying non-existence in restricted number-theoretic settings. As an application, we sketch a quantum communication protocol based on an oracle encoding of a large magic-square solution.

In non-relativistic mechanics, the total (orbital) angular momentum (AM) of a spatially-distributed system can be decomposed into intrinsic and extrinsic contributions. In relativistic quantum mechanics, intrinsic AM is typically associated with spin, which can be described using the Pauli-Lubanski four-vector. Here, we develop a unified formalism that combines the main features of both approaches and describes the intrinsic AM of a relativistic wavepacket, including both spin and orbital contributions. Our approach is based on the "expectation Pauli-Lubanski vector" constructed from the expectation values of the wavepacket's momentum and AM. Equivalently, it defines the intrinsic AM relative to the wavepacket's energy centroid. In contrast to the conventional Pauli-Lubanski formalism, the zero-mass singularity does not occur for the expectation Pauli-Lubanski vector. Consequently, the intrinsic AM of a wavepacket may have an arbitrary orientation with respect to its momentum, even for massless particles. We illustrate the general theory with a number of examples of relativistic wave beams and packets carrying spin and orbital AM.

A variational framework for the quantization of gravitational fields is developed based on an extension of the stationary action principle. Within this framework, the Wheeler-DeWitt equation for the gravitational wave functional is recovered without assuming operator promotion of the canonical momentum, thus avoiding the ambiguity of operator ordering in canonical quantization. The derivation is based on three main ingredients. First, motivated by information-theoretic considerations, the classical stationary action principle is generalized by incorporating a correction term constructed from the relative entropy associated with field fluctuations. Second, an ensemble formulation on superspace is enhanced to incorporate this entropy correction. Third, the formalism is further refined to provide a unified treatment of quantization and constraints, thereby addressing the long-standing ambiguity concerning the ordering of quantization and constraint reduction. The framework is then applied to gravitational fields coupled to a massless scalar field. Using an emergent time parameter defined via the rate equation of the gravitational fields, a Schrodinger equation for the scalar-field wave functional is recovered, supplemented by an additional quantum correction term suppressed at order $G\hbar^2$. Finally, we comment on possible connections between the notion of relative entropy employed here and holographic dualities in quantum gravity.