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.

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.

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 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.

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.

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.

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.

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 $L$.

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 $\epsilon$-approximation of a smooth function $f$ can be block-encoded using $O(\log(1/\epsilon))$ 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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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 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.

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.

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 ($\gamma$) and kinematic viscosity ($\nu$) 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 ($\Delta t_{\rm cg} > 0$), 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.

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.

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 $1<\alpha\le2$. 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 $I_p^{1+1/\alpha}$ and introduces a characteristic $\sin(\pi/\alpha)$ 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.

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 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 ($\varphi = \pi$) 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.

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.

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 \[ \FW(\z,t)=\E_{\Pp}[W_t\delta(\z-\z_t)], \qquad \z=(q,p), \] 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.

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.

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.

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.

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.

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.

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.

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 $\sigma_{\min}(J^{(\mathrm{par})}) > 0$ 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.

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.

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.

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.

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 $O(\log N)$.

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.

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.

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.

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 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 $p=1.1811 \times 10^{-17}$.

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 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.

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.

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.

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 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.

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 $T_1\approx500\,\mu$s relaxation time in the biased-noise regime (with a Ramsey dephasing time of $T^{R}_\varphi\approx90\,$ns), while an average $T_1\approx27\,\mu$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.

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 $\chi^2$-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.

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.

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 $\left |\langle\phi|U|\psi\rangle\right |^2$. In particular, we demonstrate an interpretation of these circuits as \emph{verifier circuits} with application to circuit-level device calibration.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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 $h^2(\omega)$ for the modular operator. The resulting analytic families approach the Tsirelson bound in the vacuum state as their spectral weight concentrates near $\omega\approx0$, corresponding to the eigenvalue $\lambda^2 \approx 1$ of the modular operator.

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.

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.

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.

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.

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.

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 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.

We present a modular hierarchy of private delegated quantum computation protocols tailored to user-level and industry-level settings and parameterized by the quantum resources available to the client. For each protocol, we specify the client capabilities, delegated gate set, adversarial model, transcript leakage and resulting privacy claims. The hierarchy separates QOTP state privacy under declared leakage from leakage-dependent transcript-level angle ambiguity, compiler- and leakage-function-dependent structural privacy, and output privacy, clarifies when public Clifford operations can be evaluated on quantum-one-time-pad encrypted data by classical key updates, and identifies where non-Clifford privacy, non-collusion or additional primitives are required. The classical-client branch uses a persistent common-node, matching-hidden split-QOTP together with shuffled finite-grid $r$-share sign-randomized angle sharing to obtain leakage-relative state hiding under an explicit $\epsilon_{\mathrm{key}}$ key-hiding condition and transcript-level unlinkability under hidden-matching assumptions under an explicit non-total-collusion and leakage model. The angle-sharing primitives provide transcript ambiguity under explicit leakage assumptions, not universal blindness. The trap-based layer provides detection under stated assumptions, but it is not a stand-alone malicious-security proof.

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation. As a multivariable version of QSP, multivariable quantum signal processing (M-QSP) is proposed. M-QSP interleaves signal operators corresponding to each variable with signal processing operators, which provides an efficient means to perform multivariable polynomial transformations. However, the necessary and sufficient condition for what types of polynomials can be constructed by M-QSP is unknown. In this paper, we propose a classical algorithm to determine whether a given pair of multivariable Laurent polynomials can be implemented by M-QSP, which returns True or False. As one of the most important properties of this algorithm, its returning True is the necessary and sufficient condition. The proposed classical algorithm runs in polynomial time in the number of variables and signal operators. Our algorithm also provides a constructive method to select the necessary parameters for implementing M-QSP. These findings offer valuable insights for identifying practical applications of M-QSP.

IQPopt is a software package designed to optimize large-scale instantaneous quantum polynomial circuits on classical hardware. By exploiting an efficient classical simulation algorithm for expectation value estimation, circuits with thousands of qubits and millions of gates can be optimized, provided the relevant objective function has an efficient description in terms of Pauli-Z type observables. Since sampling from instantaneous quantum polynomial circuits is widely believed to be hard for classical computers, this provides a method to identify powerful circuit instances before deployment and sampling on quantum hardware, where computational advantages may exist. The package leverages automatic differentiation in JAX, can be accelerated with access to hardware accelerators such as graphics processing units, and contains a dedicated module that can be used to train and evaluate quantum generative models via the maximum mean discrepancy.

Multipass cells enable long optical path lengths in compact volumes and are central to quantum technologies such as atomic magnetometers and optical quantum memories. In optical magnetometry, multipass geometries enhance sensitivity by increasing optical depth, reducing photon shot noise, and enabling quantum non-demolition detection. However, in conventional cylindrical multipass cells, Lissajous beam trajectories lead to repeated revisiting and incomplete mirror coverage, limiting effective volume utilization. Here we present a recirculating multipass alkali cell that overcomes these limitations by increasing the active-to-cell volume ratio and minimizing beam spot overlap. We develop an analytical ABCD-matrix model to predict beam trajectories, spot sizes, and astigmatism, validated by Zemax simulations. We further introduce a general analytical framework for spin correlation noise that incorporates astigmatism and spatial intensity distributions. By deriving the spin-noise time-correlation function and spectrum, we show how beam intensity profiles influence spin diffusion noise. Our results demonstrate improved beam coverage, reduced spot overlap, and enhanced spin correlation, particularly for concave mirrors with long focal lengths, while showing that avoiding tightly-focused regions significantly suppresses spin diffusion noise. These findings establish recirculating multipass cells as a practical, high-performance platform for precision atomic sensing and other multipass-cavity-based quantum devices.

Quantum neural networks (QNNs) are widely employed as ansätze for solving variational problems, where their expressivity directly impacts performance. Yet, accurately characterizing QNN expressivity remains an open challenge, impeding the optimal design of quantum circuits. In this work, we introduce the effective rank, denoted as $\kappa$, as a novel quantitative measure of expressivity. Specifically, $\kappa$ captures the number of effectively independent parameters among all the variational parameters in a parameterized quantum circuit, thus reflecting the true degrees of freedom contributing to expressivity. Through a systematic analysis considering circuit architecture, input data distributions, and measurement protocols, we demonstrate that $\kappa$ can saturate its theoretical upper bound, $d_n=4^n-1$, for an $n$-qubit system when each of the three factors is optimally expressive. This result provides a rigorous framework for assessing QNN expressivity and quantifying their functional capacity. Building on these theoretical insights, and motivated by the vast and highly structured nature of the circuit design space, we employ $\kappa$ as a guiding metric for the automated design of highly expressive quantum circuit configurations. To this end, we develop a reinforcement learning framework featuring a self-attention transformer agent that autonomously explores and optimizes circuit architectures. By integrating theoretical characterization with practical optimization, our work establishes $\kappa$ as a robust tool for quantifying QNN expressivity and demonstrates the effectiveness of reinforcement learning in designing high-performance quantum circuits. This study paves the way for building more expressive QNN architectures, ultimately enhancing the capabilities of quantum machine learning.

Optical technology is a highly promising platform for quantum computing due to its enormous potential for large-scale, ultrafast computation. However, realizing a programmable and scalable system remains a significant challenge. Here, we present a high-speed programmable Gaussian quantum computing platform with one hundred inputs based on a continuous-variable full-stack architecture. Our system features a 100 MHz clock frequency and integrates a cloud-based interface with an open-source Python software development kit, mqc3, significantly enhancing accessibility and operational flexibility. We provide a comprehensive characterization of our system and its capabilities through multi-input and multi-step teleportation, as well as the programmable routing of quantum states across 101 input modes. This platform represents a critical milestone in scalable analog quantum information processing, offering a robust testbed for the future integration of non-Gaussian resources and the development of large-scale optical neural networks.

Quantum Fisher Information (QFI) can be used to quantify how sensitive a quantum state reacts to changes in its variational parameters, making it a natural diagnostic for algorithms such as the Quantum Approximate Optimization Algorithm (QAOA). We perform a systematic QFI analysis of QAOA for Max-Cut on cyclic and complete graphs with $N = 4 - 10$ qubits. Two mixer families are studied, RX-only and hybrid RX-RY, with depths $p = 2, 4, 6$ and $p = 3, 6, 9$, respectively, and with up to three entanglement stages implemented through cyclic- or complete-entangling patterns. Complete graphs consistently yield larger QFI eigenvalues than cyclic graphs; none of the settings reaches the Heisenberg limit ($4N^2$), but several exceed the linear bound ($4N$). Introducing entanglement primarily redistributes QFI from diagonal to off-diagonal entries: non-entangled circuits maximize per-parameter (diagonal) sensitivity, whereas entangling layers increase the covariance fraction and thus cross-parameter correlations, with diminishing returns beyond the first stage. Leveraging these observations, we propose, as a proof of concept, a QFI-Informed Mutation (QIm) heuristic that sets mutation probabilities and step sizes from the normalized diagonal QFI. On 7- and 10-qubit instances, QIm attains higher mean energies and lower variance than equal-probability and random-restart baselines over 100 runs, underscoring QFI as a lightweight, problem-aware preconditioner for QAOA and other variational quantum algorithms.

We develop foundations for a relational approach to quantum field theory (RQFT) based on the operational quantum reference frames (QRFs) framework considered in a relativistic setting. Unlike other efforts in combining QFT with QRFs, we use the latter to provide novel mathematical and conceptual foundations for the former. We focus on scalar fields in Minkowski spacetime and discuss the emergence of relational local (bounded) observables and (pointwise) fields from the consideration of Poincaré-covariant (quantum) frame observables defined over the space of (classical) inertial reference frames. We recover a relational notion of Poincaré covariance, with transformations on the system directly linked to the state preparations of the QRF. We introduce and analyse various causality conditions, and construct an explicit example of a covariant scalar relational quantum field which is causal relative to operationally meaningful preparations of a relativistic QRF. The theory makes direct contact with established foundational approaches to QFT. We demonstrate that the vacuum expectation values derived within our framework reproduce many of the essential properties of Wightman functions and carry out a detailed comparison of the proposed formalism with Wightman QFT with the frame smearing functions describing the QRF's localisation uncertainty playing the role of the Wightmanian test functions. We also show how the properties of algebras generated by relational local observables suitably extend the core axioms of Algebraic QFT. This work is an early step in revisiting the mathematical foundations of QFT from a relational and operational perspective.

We investigate the dynamics of genuine multipartite entanglement (GME) in a system of $n$ qubits ($n\ge3$) collectively interacting with a common zero temperature bosonic bath characterized by a Lorentzian spectral density. Restricting the dynamics to the single excitation sector, the collective system-bath coupling naturally separates the Hilbert space into a superradiant mode and a subspace of states orthogonal to it, which forms a decoherence free (subradiant) subspace. We show that this symmetry induced structure leads to persistent components of the state that remain protected from dissipation. Specifically, in the three qubit case, the time evolution of genuine tripartite entanglement is analyzed using the convex roof extension of negativity. We identify parameter regimes determined by the bath spectral density and collective coupling strengths that correspond to Markovian and non-Markovian dynamics. In the Markovian limit, we demonstrate that GME can exhibit a nontrivial revival even in the absence of environmental memory effects. This revival arises from the destructive interference between the decaying superradiant component and the invariant subradiant subspace under suitable system configuration, leading to a transient loss of GME.

Multiscale organization is a hallmark of fluid turbulence in aerospace, energy, and transport systems. While quantum computing promises exponential speedups for solving the evolution equations governing flow fields, this potential is fundamentally hindered by the quantum state preparation bottleneck, the prohibitive cost of loading classical complex data into quantum states. Here, we overcome this barrier by introducing a physics-informed, three-stage geometric encoding method "turbuloscope", which efficiently generates turbulent fields relevant to high-Reynolds-number engineering flows. Rather than brute-force data loading, our approach acts as a kaleidoscope, leveraging the multiscale structures of turbulence. We capture scale-invariant self-similarity via a hyperplane approximation in high-dimensional feature space, and utilize the Hopf fibration to map quantum observables directly onto vortex tubes, the fundamental building blocks of turbulence that control mixing, drag, and heat transfer in mechanical systems. Remarkably, the algorithm requires no ancillary qubits, utilizes a linear-depth quantum circuit, and scales logarithmically with the Reynolds number, an exponential speedup compared to classical methods. We demonstrate the power of this method by generating an instantaneous turbulent field at a high Reynolds number of 35,000 across over one billion grid points using only 30 qubits, reproducing Kolmogorov's 5/3 energy spectrum, tangled vortex structures, and strong intermittency. This asymptotically optimal approach not only signals a near-term pathway to practical quantum advantage in engineering simulation, but establishes a scalable foundation for the quantum simulation of broad multiscale systems.

The Petz recovery map is a central construct in quantum information theory, providing an explicit, channel-aware prescription for reversing the effects of noise. Unlike standard quantum operations, the Petz map is intrinsically dependent on a chosen reference state, which makes its physical implementation and experimental validation particularly challenging. Here, we report an experimental realization of Petz recovery maps on a nuclear magnetic resonance (NMR) quantum processor using the duality quantum computing (DQC) algorithm. We investigate two paradigmatic single-qubit noise models: amplitude damping and phase damping, and construct corresponding families of Petz recovery maps for varying reference states. By systematically tuning the reference state, we experimentally demonstrate the state-adapted nature of Petz recovery, observing both enhanced recovery when the reference state is well matched and fidelity degradation for mismatched choices. Our experimental results show close quantitative agreement with theoretical predictions, providing direct evidence that the Petz recovery map constitutes a physically realizable, reference-state-dependent recovery channel rather than a purely formal inverse of noise. This work bridges the gap between the abstract information-theoretic formulation of Petz recovery and its implementation on a realistic quantum platform, and establishes an experimental benchmark for testing noise-adapted recovery strategies on near-term quantum devices.

We study Boundary time crystals (BTCs) in the presence of non-Markovian dynamics. In contrast to BTCs observed in earlier works in the Markovian regime, we show that non-Markovian dynamics can be highly beneficial for stabilizing BTCs over a wide range of parameter values, even in the presence of intermediate rates of dissipation. Notably, we also observe the emergence of higher-order limit cycles (HO-LCs) for some parameter regimes. We analyze the effect of non-Markovian dynamics on BTCs and HO-LCs using quantum Fisher information, time-averaged magnetization, a measure of non-Markovianity, and a dynamical phase diagram, all of which show complex behaviors with changing non-Markovianity parameters. Our studies can pave the way for stabilizing time crystals in dissipative systems, as well as lead to studies on varied dissipative dynamics on time translational symmetry breaking.

Angle encoding has emerged as a popular feature map for embedding classical data into quantum models, naturally generating truncated Fourier series with universal function approximation capabilities. Despite this expressive capability, practical training faces significant challenges. Through controlled experiments with white-box target functions, we demonstrate that training failures can occur even when all established parameter sufficiency conditions are satisfied. Building on the redundancy-gradient framework of Duffy and Jastrzebski, we provide systematic experimental evidence that non-unique frequencies dominate the gradient landscape and crowd out target frequencies -- a burden that grows exponentially with encoding depth under unary encoding. Small-angle initialization mitigates this in one-dimensional settings but fails to scale to higher dimensions, where even ternary encoding -- which minimizes per-frequency redundancy -- faces intractable combinatorial growth of unique frequency tuples regardless of initialization or optimizer choice. We introduce frequency selection as a principled solution that restricts the model spectrum to only those frequencies present in the target function. For two-dimensional targets, frequency selection achieves near-optimal performance (median $R^2 \approx 0.95$) where dense approaches struggle, and remains tractable at high-frequency magnitudes where dense approaches fail entirely (median $R^2 \approx 0.85$). Validation on a real-world dataset confirms the approach transfers beyond synthetic settings.

We show that the Guided Local Hamiltonian problem for stoquastic Hamiltonians is (promise) BPP-hard. The Guided Local Hamiltonian problem extends the Local Hamiltonian problem by incorporating an additional input known as a guiding state, which is promised to overlap with the ground state. For a range of local Hamiltonian families, prior work shows this problem is (promise) BQP-hard, though for stoquastic Hamiltonians, the complexity was previously unknown. We obtain our results by first reducing from quantum-inspired BPP circuits to 6-local stoquastic Hamiltonians. We prove particular classes of quantum states, known as semi-classical encoded subset states, can guide the estimation of the ground-state energy. Our analysis shows that this BPP-hardness does not depend on locality, i.e., the result holds for 2-local stoquastic Hamiltonians. Additional arguments extend this BPP-hardness to Hamiltonians restricted to a square lattice. We further show that for stoquastic Hamiltonians with a fixed local constraint on a subset of the system qubits, the Guided Local Hamiltonian problem is BQP-hard. In addition to these hardness results, we present a deterministic classical approximation algorithm for the problem under the conditions of constant promise gap, constant overlap, and constant spectral gap, when the guiding state is preparable in constant depth by a geometrically local circuit.

The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this within the framework of quantum reservoir computing by introducing a tunable $N$-qubit random circuit model, where a fraction $p$ of Clifford gates are probabilistically substituted with nonstabilizing conditional-$\hat{T}$ gates. We establish a direct correspondence between the reservoir's performance on temporal processing tasks and its entanglement spectrum statistics and long-range nonstabilizer resource content. To assess scalability, we study the scaling of the anti-flatness of states in the large-$N$ limit at a fixed circuit depth ratio $d/N \sim \mathcal{O}(1)$. This is taken as a witness to concentration of measures, a known impediment to learning in thermalizing systems. We demonstrate that the learnability and scalability of the reservoir can be continuously controlled by the parameter $p$, allowing us to navigate from classically tractable to maximally expressive quantum dynamics. These architecture-agnostic results provide a general strategy for designing tunable and expressive quantum reservoirs, highlighting how certain nonclassical properties control average-case intrinsic learnability and functionality.

Numerous mitigation methods exist for quantum noise suppression, making it challenging to identify the optimum approach for a specific application; especially as ongoing advances in hardware tuning and error correction are expected to reduce logical error rates. In order to facilitate the future-proof application-dependent comparison of mitigation methods, we develop a set of quantitative metrics that account for continual improvements in logical gate quality. We use these metrics to define qualitative criteria (e.g. scalability, efficiency, and robustness to characterised imperfections in the mitigation implementation), which we combine into application-specific certifications. We then provide a taxonomy of linear mitigation methods, characterising them by their features and requirements. Finally, we use our framework to produce and evaluate a mitigation strategy. A mitigation strategy is a collections of mitigation methods and compilation procedures designed to mitigate all relevant errors for a given piece of characterised hardware. Our example mitigation strategy is targeted at mitigating the outputs of hardware suffering from stochastic noise and/or rotational errors. We find the most significant determinant of efficient mitigation is accurate and precise characterisation.

Quantum resource theories use distillation protocols to convert less resourceful states into fully resourceful ones. However, these protocols often also generate an additional, unused output-referred to as a residual. We propose a framework for the quantum residual management, in which states discarded after a resource distillation protocol are repurposed as inputs for subsequent quantum information tasks. This approach extends conventional quantum resource theories by incorporating secondary resource extraction from residual states, thereby enhancing overall resource utility. As a concrete example, we investigate the distillation of private randomness from the residual states remaining after quantum key distribution (QKD). More specifically, we quantitatively show that after performing a well-known coherent Devetak-Winter protocol, one can locally extract private randomness from its residual. We further consider the Gottesman-Lo QKD protocol and provide the achievable rate of private randomness from the discarded states that are left after its performance. We also provide a formal framework that highlights a general principle for improving quantum resource utilization across sequential information processing tasks.

In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a quantum state input, one is interested in classifying to which subspace the state belongs. We prove that solving this learning problem is efficient on a quantum computer when the fragmentation phenomenon satisfies certain conditions. Furthermore, we give evidence supporting the classical hardness of this task by demonstrating that known dequantization techniques fail for the fragment classification problem. Consequently, this work provides a rare example of a physically motivated quantum machine learning task that is both efficient for quantum computers to perform and admits no known classical dequantization.

Discrete time crystals (DTCs) are non-equilibrium phases of matter that break the discrete time-translation symmetry and is characterized by a robust subharmonic response in periodically driven quantum systems. Here, we explore the DTC in a disorder-free, periodically kicked XXZ spin chain, which is stabilized by the Floquet strong Hilbert space fragmentation. We numerically show the period-doubling response of the conventional DTC order, and uncover a multiple-period response with beating dynamics due to the coherent interplay of multiple $\pi$-pairs in the Floquet spectrum of small-size systems. The lifetime of the DTC order exhibits independence of the driving frequency and a power-law dependence on the ZZ interaction strength. It also grows exponentially with the system size, as a hallmark of the strong fragmentation inherent to the Floquet model. We analytically reveal the approximate conservation of the magnetization and domain-wall number in the Floquet operator for the emergent strong fragmentation, which is consistent with numerical results of the dimensionality ratio of symmetry subspaces. The rigidity and phase regime of the DTC order are identified through finite-size scaling of the Floquet-spectrum-averaged mutual information, as well as via dynamical probes. Our work establishes the Floquet Hilbert space fragmentation as a disorder-free mechanism for sustaining nontrivial temporal orders in out-of-equilibrium quantum many-body systems.

Landauer's principle, a cornerstone of quantum information and thermodynamics, appears to be violated when the thermal reservoir is replaced by a squeezed thermal state (STS), owing to the additional thermodynamic resources inherently present in the squeezed state. We introduce a formal extension of the principle to such unitarily transformed thermal states. By defining an effective Hamiltonian, we rigorously establish a generalized Landauer inequality, which naturally reduces to the standard case for an ordinary thermal reservoir as a special instance. The framework further yields a consistent definition of entropy production and a proof of its non-negativity. We illustrate its utility by studying an arbitrarily moving Unruh-DeWitt detector coupled to a quantum field initially prepared in the STS. Using perturbation theory, we compute the entropy production explicitly, confirming its positivity. As a result of the symmetry breaking induced by the unitary transformation, it depends on both the proper time interval and the absolute spacetime position. Our work resolves the apparent violation of Landauer's principle with STSs. It also provides a robust tool for analyzing quantum thermodynamics in non-equilibrium and relativistic settings, with potential implications for quantum thermal machines and information protocols.

Group-equivariant quantum machine learning has emerged as a promising paradigm by incorporating symmetry into quantum models. However, constructing models simultaneously equivariant to both rotational and permutational symmetries in a principled manner remains a bottleneck. In this work, we develop a general framework for dual-equivariant gates under rotations and permutations and analyze the dimension of the resulting gate space using group representation theory. Based on this, we introduce HyQuRP, a hybrid quantum-classical neural network with dual equivariance. On 3D point cloud classification benchmarks in the sparse-point regime, HyQuRP outperforms strong classical and quantum baselines. For example, when six subsampled points are used, HyQuRP ($\sim$1.5K parameters) achieves 76.13% accuracy on the 5-class ModelNet benchmark, compared with 72.54%, 71.09%, and 71.03% for Tensor Field Network, PointNet, and PointMamba with similar parameter counts. These results highlight HyQuRP's strong data efficiency and suggest the potential of equivariant quantum machine learning approaches in symmetry-sensitive tasks.

Equilibrium statistical ensembles commute with the Hamiltonian and thus carry no coherence in the energy eigenbasis. We develop a framework in which energy fluctuations can retain genuinely quantum-coherent contributions. We foliate state space into ``minimum-variance leaves,'' defined by minimizing the average energy variance over all pure-state decompositions, with the minimum set by the quantum Fisher information. On each leaf we construct the least-biased state compatible with normalization and mean energy, defining a leaf-canonical ensemble. The Gibbs ensemble is recovered on the distinguished commuting leaf, while generic states are organized by their leaf label. This structure provides a natural setting to extend eigenstate thermalization beyond equilibrium via a ``leaf typicality'' hypothesis. According to that hypothesis, local observables depend only on the leaf and energy and are reproduced by a representative pure state drawn from the optimal ensemble, whose minimized energy spread reduces the complexity of time evolution.

Quantum error correction (QEC) promises to exponentially suppress qubit noise, but typically assumes spatially-uniform and temporally-constant noise rates. However, real quantum hardware exhibits variation in noise levels over time, which will be amplified by QEC if not addressed. To mitigate this drift in error rates, we leverage transient information readily available in surface code quantum error correction to predict logical error rates (LER) in real time. We infer a prediction model by sampling physical error rates from real hardware, and mapping detector fire rate (DFR), or parity of stabilizer measurements across QEC rounds, to LER. This allows for on-the-fly LER predictions without the typical characterization overhead required to determine LER. This method can easily be extended to other stabilizer codes. Importantly, we observe that this prediction should be accurate yet conservative (i.e. give an upper estimate) to enable appropriately fast responses to real-time physical error changes. That is, responses should be executed marginally ahead of time to allow for their execution to complete, and minimize time spent (ideally none) above intolerable error rates. More importantly, we pair this predictor with a scheme which remaps drifted logical qubits to fresh tiles in a patch-based architecture while their original tiles are recalibrated. Our results demonstrate DFR-based prediction to be an effective LER predictor, and remapping as a spatially efficient and timely mitigation response for small code distances, both of which are significant steps in furthering practical QEC.

Amplitude estimation, in its original form, is formulated as phase estimation upon the Grover iterate. Subsequent improvements to the algorithm have eliminated the need for phase estimation and introduced low-depth variants that trade speedups for lower circuit depth. We make the key observation that amplitude estimation is equivalent to estimating the energy gap of an effective Hamiltonian, whereby discrete-time evolution is generated by amplitude amplification. This enables us to develop an amplitude estimation algorithm for both Heisenberg-limited and low-depth circuit regimes, inspired by statistical phase estimation techniques developed for early fault-tolerant ground-state energy estimation. In the Heisenberg-limited regime, our approach achieves performance comparable to state-of-the-art methods while using simplified classical post-processing. In the low-depth regime, it obtains optimal query--depth tradeoffs up to polylogarithmic factors, with provable guarantees and improved empirical performance over prior approaches. The resulting protocol is ancilla-free and requires only standard Grover reflections. Due to its flexibility, generality, and robustness, we expect our approach to be a key enabler for a broad range of early fault-tolerant applications.

Quantum channels generally reduce the distinguishability of quantum states, limiting information transmission and processing. Previous work introduced a protocol capable of increasing the distinguishability of states after the action of a specific quantum channel. Here we show how to systematically determine the maximal distinguishability gain achievable by this method. We develop an algorithm that identifies the optimal implementation of the protocol and applies to arbitrary quantum channels in a straightforward manner. Using this approach, we demonstrate that a weakly non-Markovian channel can effectively be converted into an essentially non-Markovian one through a distillation-like process. We further analyze the quantitative features of the optimized protocol, characterizing the conditions under which the enhancement is most pronounced. Our results provide a general framework to assess and optimize distinguishability recovery in open quantum systems.

A fundamental obstacle to scalable solid-state quantum networks is the lack of a universal interface providing strong light-matter coupling, deterministic nonreciprocal photon routing, and efficient extraction. Here we propose a plasmonic platform overcoming these challenges using a Tomonaga-Luttinger liquid (TLL) in a single-walled carbon nanotube (SWCNT) microtoroid. The TLL's collective bosonic excitations are kinematically protected against backscattering by a large valley-momentum mismatch, guaranteeing robust chiral spin-momentum locking unattainable in dielectric cavities. This 1D protection enables deterministic routing of circularly polarized photons from a quantum emitter (e.g., a nitrogen-vacancy center) into distinct propagation channels. By aligning the emitter's symmetry axis, parasitic {\pi} transitions are geometrically forbidden. Furthermore, residual atomic-scale backscattering is suppressed to ~100 Hz via electrostatic gating and annealing. To overcome the severe mode mismatch between the CNT plasmon and optical fiber, we introduce a graded plasmonic-photonic mode converter, providing a path to near-unity extraction efficiency. Using a tripod-STIRAP scheme, we demonstrate high-fidelity, magnetically tunable spin-photon entanglement. Our analysis confirms operation deep in the strong-coupling regime, with cooperativities C > 100 and chiral contrast exceeding 20 dB. This wavelength-agnostic architecture is compatible with any solid-state emitter, establishing a scalable blueprint for robust, nonreciprocal quantum nodes in a global quantum internet.

We develop a resolvent-based self-consistent framework for strongly correlated many-body systems by reorganizing many-body expansions at the level of the resolvent rather than through perturbative expansions in a small parameter. Starting from the spectral representation of the diagonal Green's function, we derive an exact recursive hierarchy for the self-energy in terms of correlated multi-resolvent propagation processes. The resulting hierarchy remains formally closed in terms of diagonal resolvents and provides a systematically improvable description of fluctuations beyond mean-field theory. The framework contains two complementary nonperturbative structures. The Lanczos continued-fraction representation governs recursive single-resolvent renormalization and generates non-Lorentzian spectral broadening beyond conventional self-consistent Born approximations (SCBA). By contrast, the multi-resolvent hierarchy introduces correlated frequency mixing through products of resolvents and Hilbert-transform couplings, providing a microscopic mechanism for spectral asymmetry and skewness absent in parity-preserving single-resolvent closures. To solve the hierarchy, we introduce Lorentzian, Gaussian, and hybrid Voigt-type closure schemes together with an effective Faddeeva self-energy representation preserving analyticity and causality. Spectral broadening, tail structures, and higher-order fluctuation effects then emerge naturally from the interplay between recursive renormalization and multi-resolvent correlations. Unlike conventional diagrammatic resummations, the present approach does not rely on finite-order truncations or small expansion parameters. Instead, correlations are organized through an exact resolvent hierarchy combined with ETH-type statistical assumptions, making the framework particularly suitable for nonintegrable many-body systems with dense spectra.

We introduce RFOX (Rotated-Field Oscillatory eXchange), a parameter-free quantum algorithm for combinatorial optimization. RFOX combines an almost constant non-stoquastic $XX$ catalyst with a weak harmonic $ZX$ counter-diabatic term. Using the Floquet-Magnus expansion, we derive a closed-form effective Hamiltonian whose first-order term retains the full $XX$ driver, while the leading correction consists of a local single-qubit $Y$ field and poly-local 3-body topological interactions driven by the graph connectivity at high drive frequency. This structure ensures that the instantaneous spectral gap remains essentially flat, independent of both the interpolation parameter and the disorder strength, modulated only by a $\delta$ parameter. This behavior stands in stark contrast to the unpredictable gap reductions, or even collapses, exhibited by the $X$ (stoquastic), $XX$, and $X+sXX$ (non-stoquastic) driver schedules. Extensive noiseless simulations on random-field Ising model (RFIM) instances with 7, 9, and 12 qubits, across three magnetic-field ranges, validate these spectral predictions: RFOX attains near-optimal, and in some cases exact, ground states using up to an order of magnitude fewer Trotter slices. Its performance advantage grows with increasing disorder, as conventional methods slow down near vanishing gaps, whereas RFOX maintains a constant runtime scaling of $T \propto \Delta_{\min}^{-2}$. Hardware experiments on IBM Quantum processors (Eagle r3 and Heron r1, with 12, 15, and 20 physical qubits) reproduce similar performance rankings. These results suggest that fixed-gap, non-stoquastic drivers augmented with analytically derived counter-diabatic terms offer a promising, scalable, and tuning-free route toward quantum optimizers for combinatorial optimization problems.

We study the task of lifting arbitrary quantum states and channels to purifications and Stinespring dilations, respectively, in both the probabilistic exact and deterministic approximate settings. We formalize this task through a general framework of quantum purification machines that, given a finite number of copies or uses of a black-box input, aim to output a corresponding purification or Stinespring dilation. In the probabilistic exact setting, we show that universality is not necessary to rule out such transformations: the simple requirement that a machine purifies two inputs of different rank with non-zero probability already implies that it cannot be described by a linear positive map. This simple argument captures a fundamental obstruction of quantum theory and recovers the impossibility of universal probabilistic purification from finitely many copies. In the approximate setting, we allow for general machines that are not required, in general, to produce a pure output. Using the minimum average error as our figure of merit, we derive analytical expressions for the performance of several physically motivated strategies as well as a general upper bound on the achievable error, which is tight in a specific regime. Our analysis reveals a trade-off: strategies that produce a pure output - among which we prove the optimal to be a strategy that produces as a fixed output a maximally entangled purification of the fully depolarizing channel - perform optimally between those considered for large environment dimension, while append-environment strategies that generally produce non-pure outputs perform better at small environment dimension.

We derive an upper bound on the maximum balanced bipartite entanglement entropy of ground states of many-body Hamiltonians defined on a graph, agnostic to any particular model, that possesses a nontrivial automorphism group. We show that the entropy is bounded by the logarithm of a weighted sum of multiplicities of irreducible representations of the bipartition-preserving automorphism subgroup. This bound complements the known degeneracy-based bound, with neither universally dominating the other. For the complete graph $K_n$, the new bound yields an exponential improvement from linear to logarithmic scaling in the system size, consistent with the exact value of the entropy.

The efficient execution of fault-tolerant quantum algorithms is fundamentally limited by the production rate of magic states required for non-Clifford operations. While circuit optimization typically targets T-depth, static T-depth does not reliably predict executable performance under bounded T-state delivery. We introduce a model that captures demand-supply imbalance using two key quantities: slack ratio, a structural indicator of scheduling flexibility, and Delta_max, a measure of cumulative demand surplus. We show that Delta_max is a strong schedule-level indicator of execution slowdown and yields a provable lower bound on executable makespan for a fixed schedule. Empirical evaluation on constructed directed acyclic graph (DAG) families, with arithmetic circuits and exact quantum Fourier transform (QFT) traces providing additional grounding, shows that slack ratio is a stronger structural predictor than T-depth for stall and inversion risk, while Delta_max is the strongest predictor of slowdown. Across 4,904 instances, the lower bound shows zero violations, with 88.9% of cases within one cycle. These results highlight the importance of explicitly modeling delivery constraints in fault-tolerant quantum compilation.

Catalytic quantum error correction (CQEC) recovers quantum states via catalytic covariant transformations but requires full knowledge of the target state. We introduce blind CQEC, which estimates the target from the noisy output alone before catalytic recovery. Five estimation strategies are benchmarked across three noise models (dephasing, depolarizing, amplitude damping), four quantum algorithms ($d = $4-64), Haar-random states up to $d = 256$, and mixed-state targets with variable purity. Key results: (i)coherence maximization achieves $F_{rec} > 0.95$ for $d \leq 16$ without noise-model knowledge, matching the oracle to within $4\%$; (ii)channel inversion is required at $d = 64 (F_{rec} = 0.905$); (iii)estimation and recovery fidelities are linearly correlated ($r > 0.99$), identifying target estimation as the sole bottleneck; (iv)an analytical crossover dimension $d^* \approx $25-40 separates noise-model-free and noise-informed regimes, bridged by a hybrid interpolation strategy; (v)copy scaling follows $1 - F(n) \sim n^{-\alpha}$ with $\alpha \in [0.4, 2.2]$, spanning the statistical averaging and denoising synergy limits. Direct comparison with standard quantum error mitigation (ZNE, PEC, virtual distillation) shows that blind coherence maximization uniquely achieves state-level recovery without noise-model knowledge, while blind channel inversion matches PEC's fidelity at single-copy overhead. An end-to-end VQE demonstration for H$_2$ shows $3.4\times$ energy-error reduction with channel-inversion blind CQEC, and a circuit-level sanity check on qiskit-aer confirms that the density-matrix predictions translate to small noisy circuits. We also derive an analytical Lipschitz bound $F_{rec} \geq 1 - 2\|\hat{\rho}_{est} - \rho_{target}\|_1$ for the density-matrix-level recovery map, providing the theoretical underpinning for the empirical estimation-recovery correlation.

We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error correction. The exploration employs $3+2$ particles on nested squares proposed in the companion letter (arXiv:2504.07941), where three of them encode Shor's nine-qubit code and the remaining two detect errors in this code through their spin state measurements (unlike the letter's quantum walk model, each particle evolves by gate operations acting exclusively on either its spin or position state). The first result is that the GS offers resilience against three types of noise acting on a particle: arbitrary decoherence of its spin or position state, and dephasing of both states, which partly or completely destroys its QSD. To show that, we formulate a noise model unifying the above noise and prove the correctability of this unified model under our error-correcting scheme. The second result is that QSD provides architectural flexibility allowing us to stack the error-correcting systems both vertically and horizontally. Indeed, we show implementations of the error detection (stabilizer measurement), logical Hadamard and Toffoli gates, and a quantum adder with the required interactions only between nearest-neighbor and next-nearest-neighbor particles.

We study coordination under restricted information, where classical local models fail to implement certain correlated distributions because agents cannot condition on past history. We show that quantum systems overcome this limitation even when using only separable states. Both classically diagonal encodings (shared latent variables) and separable states with noncommuting local structure (quantum discord) enable the implementation of joint distributions that are unattainable by any classical local rules under the same information constraints. The quantum advantage arises from enabling latent-variable coordination without requiring agents to condition on the latent variable itself -- a construction that succeeds where no classical local model can. Separable states with nonzero quantum discord provide an alternative mechanism for realizing such coordination. At the same time, quantum models remain strictly limited by the information structure: unlike perfect recall, they cannot reproduce fully adaptive dependence on realized past outcomes that are observationally indistinguishable. Thus, quantum correlations serve as a partial substitute for perfect recall.

Continuous-variable quantum key distribution (CVQKD) using passive state preparation (PSP) offers low-cost, high-rate secure communication. However, the existing PSP-CVQKD scheme with a transmitted local oscillator has high photon leakage noise and poor stability, making it unsuitable for high-loss transmission. In this work, for the first time, we propose and implement a local local oscillator (LLO) CVQKD system using a self-referenced (SR) PSP scheme, and give a theoretical proof of the equivalence of the PSP and GMCS protocol using temporal-mode theory. By employing the novel self-referenced pilot scheme to achieve high-precision time-varying frequency and phase compensation algorithms, we significantly improve the system' s signal-to-noise ratio and stability. The system achieves a record-high asymptotic secret key rate of 10.34 Mbps over a free-space channel with up to 23.5 dB loss, while maintaining low excess noise and robust performance under turbulent conditions. This work establishes the feasibility of SR-LLO CVQKD, providing a practical pathway toward secure, high-rate quantum communication in realistic environments.

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.

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 construct many-body scar states in multi-flavour fermionic lattice models that possess strong magnetic or superconducting correlations of a given type specified by a unitary matrix $A$. One of the states maximizes the one-point correlations over the full Hilbert space and has the form of the BCS wavefunction. It may always be made the ground state by adding the correlations as a "pairing potential" to any Hamiltonian supporting group-invariant scars. In our single-flavour, spin-full fermions example we consider a superconducting $A$. The BCS scar ground state is a linear combination of the well-known $\eta$-pairing states. In the multi-orbital fermions example the BCS-like ground state maximizes unconventional magnetic correlations. The broad class of eligible Hamiltonians includes many conventional condensed matter interactions. The part of the Hamiltonian that governs the exact dynamics of the scar subspace coincides with the BCS mean-field Hamiltonian. We therefore show that its eigenstates are many-body scars that are decoupled from the rest of the Hilbert space and thereby protected from thermalization. Our results point out a connection between the fields of superconductivity and weak ergodicity breaking (many-body scars) and will hopefully encourage further investigations. They also provide the first feasible protocol to initialize a fermionic system to a scar state in (a quantum simulator) experiment.

The Casimir force follows from quantum fluctuations of the electromagnetic field and yields a nonlinear attractive force between closely spaced conductive objects. Measuring the Casimir force in superconducting materials on either side of the transition should allow to isolate the specific contribution of low frequencies to the Casimir effect. There is significant interest in this contribution as it is suspected to be involved in an unexplained discrepancy between predictions and measurements of the Casimir force between normal metals. Here, we observe a force acting on a superconducting drum resonator integrated in a microwave optomechanical cavity through the nonlinear dynamics this force imparts to the resonator. The measured dynamics points to an extremely intense force found to be compatible in magnitude with the Casimir force for the range of vacuum separations that can be expected in this device, and incompatible with estimates of other known sources of nonlinearity. This nonlinearity is intense enough that, with a modified design, this device type should operate in the single-phonon nonlinear regime. Accessing this regime has been a long-standing goal that would greatly facilitate quantum operations of mechanical resonators.

We obtain the Green's function for fermions in an external non-Abelian gauge field with an $SU(N)$ symmetry group. As an external field, we examine the solution to the Yang-Mills equation presented as a plane wave on the light cone.

We study a broad class of qudit stabilizer codes, termed $\mathbb{Z}_N$ bivariate-bicycle (BB) codes, arising either as two-dimensional realizations of modulated gauge theories or as $\mathbb{Z}_N$ generalizations of binary BB codes. Our central finding, derived from the polynomial representation, is that the essential topological properties of these $\mathbb{Z}_N$ codes can be determined by the properties of their $\mathbb{Z}_p$ counterparts, where $p$ are the prime factors of $N$, even when $N$ contains prime powers ($N = \prod_i p_i^{k_i}$). This result yields a significant simplification by leveraging the well-studied framework of codes with prime qudit dimensions. In particular, this insight directly enables the generalization of the algebraic-geometric methods (e.g., the Bernstein-Khovanskii-Kushnirenko theorem) to determine anyon fusion rules in the general qudit situation. Moreover, we elucidate the symmetry-enriched topological (SET) order underlying the quasifractonic behavior in qudit BB codes (including the Delfino-Chamon-You model), resolving the associated anyon mobility puzzle. We also develop an efficient computational algebraic method, based on Gröbner bases over the ring of integers, to determine both the topological order and its SET properties.

Topological states of matter in disordered systems without translation symmetry have attracted great interest in recent years. These states with topological characters are not only robust against certain disorders, but also can be counterintuitively induced by disorders from a topologically trivial phase in the clean limit. In this review, we summarize the current theoretical and experimental progress on disorder-induced topological phases in both condensed-matter and artificial systems. We first introduce the topological Anderson insulators (TAIs) induced by random disorders and their topological characterizations and experimental realizations. We then discuss various extensions of TAIs with unique localization phenomena in quasiperiodic and non-Hermitian systems. We also review the theoretical and experimental studies on the disorder-induced topology in dynamical and many-body systems, including topological Anderson-Thouless pumps, disordered correlated topological insulators and average-symmetry protected topological orders acting as interacting TAI phases. Finally, we conclude the review by highlighting potential directions for future explorations.

Neutral atoms have become a competitive platform for quantum metrology, simulation, sensing, and computing. Current magic trapping techniques are insufficient to engineer magic trapping conditions for qudits encoded in hyperfine states with $J \neq 0$, compromising qudit coherence. In this paper we propose a scheme to engineer magic trapping conditions for qudits via bichromatic tweezers. We show it is possible to suppress differential light shifts across all magnetic sublevels of the $5s5p$ $\mathrm{^{3}P_2}$ state by using two carefully chosen wavelengths (with comparable tensor light shift magnitude and opposite sign) at an appropriate intensity ratio, thus suppressing light-shift induced dephasing, enabling scalar magic conditions between the ground state and $5s5p$ $\mathrm{^{3}P_2}$, and tensor magic conditions for qudits encoded within it. Furthermore, this technique enables robust operation at the tensor magic angle 54.7$^\circ$ with linear trap polarization via reduced sensitivity to uncertainty in experimental parameters. We expect this technique to enable new loading protocols, enhance cooling efficiency, and enhance nuclear spins' coherence times, thus facilitating qudit-based quantum computing in ${}^{87}$Sr in the $5s5p$ $\mathrm{^{3}P_2}$ manifold.

Deep generative modeling to stochastically design small molecules is an emerging technology for accelerating drug discovery and development. However, one major issue in molecular generative models is their lower frequency of drug-like compounds. To resolve this problem, we developed a novel framework for optimization of deep generative models integrated with a D-Wave quantum annealing computer, where our Neural Hash Function (NHF) presented herein is used both as the regularization and binarization schemes simultaneously, of which the latter is for transformation between continuous and discrete signals of the classical and quantum neural networks, respectively, in the error evaluation (i.e., objective) function. The compounds generated via the quantum-annealing generative models exhibited higher quality in both validity and drug-likeness than those generated via the fully-classical models, and was further indicated to exceed even the training data in terms of drug-likeness features, without any restraints and conditions to deliberately induce such an optimization. These results indicated an advantage of quantum annealing to aim at a stochastic generator integrated with our novel neural network architectures, for the extended performance of feature space sampling and extraction of characteristic features in drug design.

We investigate the integrable structure and soliton dynamics of a coupled modified Korteweg-de Vries (cmKdV) system with a real symmetric coupling matrix. We introduce a vector reformulation of Hirota's bilinear formalism in which both the bilinear equations and their solutions are expressed directly at the vector level, rather than through a component-wise construction. This formulation preserves the intrinsic structure of the coupled system and provides a compact framework for multi-component nonlinear wave dynamics. Within this approach, we construct explicit one-, two-, and three-soliton solutions in closed vector form and recover the three-soliton condition directly at the vector level, confirming consistency with integrability. The method enables a unified treatment of focusing, defocusing, and mixed-sign regimes. In particular, for indefinite coupling, it reveals the existence of nontrivial vector ground states, leading to soliton solutions on non-zero backgrounds. These results highlight the structural advantages of the vector bilinear approach and open perspectives for the study of more general nonlinear excitations in multi-component integrable systems.

Non-invertible symmetries of a quantum field theory (QFT) are a natural generalization of unitary symmetries, but in which the product of operators does not satisfy a group multiplication law. We show that such symmetry operations on states define a collection of quantum gates for a parallel quantum computation scheme that includes post-selection / projection as a gate. Structures such as gate complexity and more geometric complexity measures generalize to this setting. We provide a class of distance / distinguishability measures that extend the standard notion of distance for Lie groups to both continuous and discrete non-invertible symmetries, as well as more general linear combinations of unitary quantum gates. We illustrate these considerations by computing the distance between non-invertible symmetries in some 4D and 2D QFTs. We find that the simple objects of a symmetry category can be highly complex computationally.

Weber's conjecture (1886) governs three aspects of lattice-based cryptography: the solvability of the Principal Ideal Problem, the freeness of modules over rings of integers, and the tightness of worst-case-to-average-case reductions in Ring-LWE (R-LWE) and Module-LWE (MLWE). Existing verifications for $k \ge 9$ rely on Generalized Riemann Hypothesis (GRH). In this paper, we present the first unconditional proof for $k \le 12$. Our method combines the Fukuda-Komatsu computational sieve, inductive structure of the cyclotomic $\mathbb{Z}_2$-tower, and Herbrand's theorem.