Quantum Physics Paper Analysis

Distinguishability is a central concept in information theory and extends naturally to quantum systems. This work shows that, for any two finite-dimensional memoryless quantum channels, parallel, adaptive and general testing strategies achieve the same Stein exponent at every fixed type-I error tolerance $ε\in(0,1)$, namely the regularized channel relative entropy. When this rate is finite, any larger type-II exponent forces the probability of correctly accepting the null hypothesis to decay exponentially. Thus, adaptivity provides no asymptotic advantage. The key step is proving the continuity of the regularized sandwiched Rényi channel divergence at order one. We also derive the exact strong-converse exponent for general testers.

Feature selection is an essential step for reducing complexity of high dimensional data, usually in preparation for developing machine learning models such as computational biomarkers. However, there are limitations associated with feature selection such as for metabolomic data where there are hundreds or even thousands of features per study participant, while the available number of participants in a clinical trials is limited. Classical methods such as exhaustive search require evaluation of all possible feature combinations, making them costly in terms of computation and runtime, or even infeasible, as feature dimensionality increases. In this study, we propose a novel Quadratic Unconstrained Binary Optimization (QUBO) coefficient formulation and pose metabolomic feature selection as a QUBO problem that selects a specified number of features by balancing their relevance against redundancy among the selected variables. To evaluate our proposed QUBO objective function, we conducted a series of experiments using Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO) and Quantum Approximate Optimization Algorithm (QAOA) on a quantum gate based computer. We also compared the method to several classical methods on three metabolomic datasets associated with Autism Spectrum Disorder (ASD) on a classical computer. Our method reduces runtime compared with exhaustive search and Iterative Tabu Search (ITS) and achieves competitive performance across classifiers compared to classical filter, wrapper, and embedded methods. These results do not claim quantum advantage; rather, they establish hardware feasibility and demonstrate the current capabilities of Noisy Intermediate-Scale Quantum (NISQ) devices.

A key challenge in quantum cryptography is to build quantum one-wayness and pseudorandomness without the use of (quantum computable) one-way functions. So far, this has turned out to be a difficult task, with only a few proposed candidates that are not directly built from one-way functions. Even within these few proposed candidates, we have lacked the techniques to analyze when proposed constructions may inadvertently yield one-way functions. In this work, we introduce efficient NP-aided shadow tomography of quantum states. We prove that collections of {\em computable} pure states can be learned via efficient NP-aided shadow tomography, where we say that a state is computable if the amplitude and phase on any computational basis term can be classically efficiently computed given the description of an efficient preparation circuit for the state. We also give new algorithms for NP-aided learning of unitaries given polynomially many queries to the unitary. By building on this, we show that many existing architectures for PRS and PRU, including some that were explicitly introduced for the purposes of avoiding one-way functions (e.g., Hamiltonian Phase States, Bostanci et. al., TQC 2025), actually do imply the existence of one-way functions or imply \(\NP\) hardness. We hope that these no-go results will inform future investigations into building PRS and PRUs from assumptions that are plausibly outside the complexity class NP.

Recent advances in quantum simulation have enabled the discovery of novel forms of universality in quantum many-body dynamics. In this Review, we discuss deep thermalization and Hilbert space ergodicity--two recently discovered phenomena characterized by the emergence of distributions of quantum states that are "maximally random" in a precise sense. They offer a new perspective on how irreversible statistical mechanics arises from reversible unitary quantum dynamics, going beyond conventional theories of quantum thermalization and equilibration. We review a unifying framework, rooted in quantum information theory and principles of maximum entropy, that explains the different forms of ergodicity which arise under various physical constraints. We discuss open questions and active research directions, including generalizations beyond ensembles of pure quantum states, phase transitions in deep thermalization tied to deeper forms of ergodicity-breaking, connections to broader topics in quantum thermalization and ergodicity, and applications in quantum information science, such as for benchmarking or tomography.

We describe a family of convex uniformly continuous functions $E^λ_F$, $λ>0$, on the set of states of a bipartite quantum system (consisting of finite-dimensional or infinite-dimensional subsystems), which monotonically increase and converge pointwise to the Entanglement of Formation (EoF) as $λ\to0$. These functions are "nonselective" entanglement monotones defined by the way close to the construction of the Moreau-Yosida regularization (the Moreau envelope) of a convex function on a convex set used in the modern convex analysis. So, we call the functions $E^λ_F$ the Moreau-Yosida approximations of the EoF and describe their equivalent definitions and basic properties. The semicontinuity bounds for the EoF (presented in [Lob.J.Math., 46(6), 2632-2658]) allow us to obtain easily computable upper bounds on the difference $E_F(ρ)-E^λ_F(ρ)$ for a given state $ρ$. These bounds give easily computable bounds on the rate of uniform convergence of the function $E^λ_F$ to the EoF as $λ\to0^+$ on the sets of states with bounded rank/energy of one of the marginal states. We also discuss sufficient conditions for the coincidence of $E_F(ρ)$ and $E^λ_F(ρ)$ at a given state $ρ$ for all $λ$ small enough and consider several classes of states for which such coincidence takes place. The conjectured selective LOCC-monotonicity of the functions $E^λ_F$ and a possible way to prove it are briefly discussed. Secondary parts of the article are written with the help of ChatGPT-5.6.

We propose a variational framework for the efficient simulation of stochastic quantum dynamics in interacting bosonic systems. Our method generalizes the time-dependent variational principle to accommodate quantum state diffusion processes and is tailored for describing quantum trajectories unraveled from a master equation. We adopt a wavefunction ansatz composed of a coherent superposition of Gaussian wavepackets, which allows the fully analytical assembly of the variational equations of motion while capturing both the quantum trajectory dynamics and the Lindblad evolution beyond semiclassical approximations. The method is carefully benchmarked on a Bose-Hubbard dimer, and applied to extended Bose-Hubbard lattices in both 1D and 2D. In particular, we show the emergence of a symmetry-breaking phase transition in 2D lattices, which is absent in 1D chains.

Loan portfolio optimization (LPO) seeks portfolios that minimize credit risk while satisfying practical selection constraints. Accounting for portfolio-level risk requires modeling not only expected losses but also loss variability and borrower-default correlations, leading to a large-scale combinatorial optimization problem whose complexity grows rapidly with portfolio size. In this work, we formulate LPO as a Quadratic Constrained Binary Optimization (QCBO) problem that jointly captures expected and unexpected losses and transform the resulting formulation into a Quadratic Unconstrained Binary Optimization (QUBO) model suitable for variational quantum optimization. To address the limited qubit resources of current quantum hardware, we employ Pauli Correlation Encoding (PCE), which enables a large number of portfolio-selection variables to be represented using comparatively few qubits. The proposed framework is evaluated on a real-world microfinance dataset comprising 2012 borrowers. For problem instances with up to 1000 portfolio-selection variables, we benchmark classical simulations of a variational quantum algorithm (VQA) against Google OR-Tools under matched time budgets, obtaining feasible portfolios with an objective-value gap of about 40% across all sizes. We further implement the framework on superconducting quantum hardware for instances containing up to 1500 variables. Across these instances, the experimentally obtained objective values are within 10% of the corresponding simulation results. These findings demonstrate the feasibility of applying PCE-based variational quantum optimization to large-scale loan portfolio optimization under current quantum hardware limitations.

Suppressing decoherence and crosstalk systematically across large networks of qubits is a pressing concern as qubit counts increase rapidly. General multi-qubit dynamical decoupling (DD) has historically been based on Hadamard matrices and orthogonal arrays, with instantaneous-pulse sequences whose circuit depth scales linearly with the number of qubits. Chromatic-Hadamard DD (CHaDD) improves upon these methods by properly coloring the hardware graph and assigning to each color a row of a Hadamard matrix, resulting in a circuit depth that scales linearly with the number of colors $C$, which can be as low as the chromatic number of the graph. Here, we explore the tradeoff between circuit depth and the pulse repetition rate (PRR), the average fraction of time steps in which a qubit is pulsed, i.e., a measure of pulse density. We introduce two single-axis sequences based on binary and Gray matrices, Chromatic-Binary DD (CBDD) and Chromatic-Gray DD (CGDD), which, for $C>2$, are special cases of non-minimum-depth CHaDD and achieve PRR $<2/C$ and PRR $=1/C$, respectively, compared with a PRR above $1/4$ for CHaDD, at the price of a circuit depth of $2^C$. In state preservation experiments on a $127$-qubit IBM processor with $C=3$, the less dense sequences outperform CHaDD at short times when the pulses are not robust; this advantage is largely eliminated by robust versions designed to compensate for coherent pulse errors, and among the robust sequences, CGDD uses the fewest pulses over a fixed protection time. Across non-robust $C=3$ and $C=5$ schedules, equal PRR on a fixed qubit subset is empirically associated with similar state preservation. Thus, the PRR serves as a practical figure of merit for chromatic DD whenever coherent pulse errors dominate.

We prove that the spectrum of an unknown $d$-dimensional quantum state can be estimated to error $\varepsilon$ in total variation distance using \[ O\!\left(d^2\min\left\{ \frac{1}{(\varepsilon\log d)^4},\; \frac{1}{(\varepsilon\log d)^2} \right\}\right) \] copies. This matches the recent lower bound of Wang. When restricted to unentangled measurements, we give an algorithm with an additional factor of $d$ in copy complexity, which we conjecture to be optimal. We develop a framework for recovering the small eigenvalues of a quantum state by matching Chebyshev moments. We bound the variance of each Chebyshev moment estimate in terms of scalar derivatives of the corresponding polynomial, using classical and quantum Efron--Stein decompositions. Different rescalings of the Chebyshev polynomials balance approximation error and variance, yielding two regimes in our copy complexity bound.

Non-Abelian quantum codes connect quantum error correction, phases of matter, and computational resources. In this work, we develop a general framework for constructing non-Abelian quantum low-density parity-check (qLDPC) codes by gauging sheaf codes via cup products and use it to obtain families with constant encoding rate and linear distance. We resolve the coupled logical constraints using explicit representatives to characterize the full gauged code space. We provide a fundamental treatment of code distance based on the general Knill--Laflamme condition and combine expansion with cleaning to establish protection against arbitrary low-weight errors. We further construct an almost-good family whose entire code space exhibits long-range magic. Gauging and ungauging also enable logical Clifford measurements that prepare encoded magic states. These results extend good qLDPC codes beyond the Pauli stabilizer setting and provide a concrete foundation for exploring non-Abelian phases beyond geometric locality and pursuing the no low-energy trivial magic conjecture.

Future quantum networks will make use of entanglement to perform numerous tasks, such as sending quantum information over long distances, distributed quantum computing, and quantum sensing. In general, these tasks will need to be performed simultaneously in various regions of a network, while minimizing resources and latency. We will thus require policies for scheduling link-level entanglement resources, and using the link-level entanglement to create various forms of multipartite entanglement required for every task. In this work, we address this problem using reinforcement learning. We formulate a Markov Decision Process for the problem and use double deep Q-networks (DQN) with Message Passing Neural Networks (MPNNs), experience replay buffers, and curriculum training to obtain policies. The key physical parameter is the probability of link-level entanglement generation, i.e., the link activation probability. We show that our policies maintain 100% success for up to 71% lower link activation probability than the baseline heuristics for a set of physically relevant network topologies. We then examine an additional constraint where experiment (task) placements are restricted to specific hardware types and demonstrate a similar advantage in performance over heuristics, with our policy maintaining at least an 80% success rate for up to a 59% lower link activation probability. Finally, we explore methods to interpret the learned policy by defining metrics enabling conclusions to be drawn about the model's behavior and by tasking a large language model (LLM) to derive a novel heuristic given example actions taken by the DQN-trained policy. We find that the LLM heuristic performs similarly to the DQN-trained policy in performance, indicating a promising method for interpretable policy extraction for large quantum networks, where direct training becomes computationally expensive.

We determine the exact universal high-temperature separability threshold for Pauli Hamiltonians of bounded degree $Δ\ge2$. If every coefficient in the Hamiltonian has magnitude at most one and each term has overlapping support with at most $Δ$ other terms, the Gibbs state is a mixture of product Pauli eigenstates whenever \[ β\le z_Δ:= \operatorname{arctanh}\left[\max_{0\le x \le 1}x\left(\frac{1-x}{1+x}\right)^{Δ-1} \right]. \] For every $β>z_Δ$, a finite commuting Hamiltonian with maximum overlap degree at most $Δ$ has an entangled Gibbs state. At any fixed $β<z_Δ$ strictly below the threshold, a classical polynomial-time algorithm produces samples from a distribution over product Pauli eigenstates approximating the Gibbs state in trace distance.

We establish proper agnostic learning of matrix product states and tree tensor networks. Given copies of an arbitrary quantum state $ρ$, our algorithms return a state $|ψ\rangle$ of chosen bond dimension such that $\langleψ| ρ|ψ\rangle$ is within $\varepsilon$ of the optimum over the model class, without assuming that $ρ$ itself belongs to or is well approximated by that class. The main idea is to use improper learning to compress the mixed-state objective, reducing proper agnostic learning to optimization against a finite collection of explicitly specified pure states. We then introduce a comparator-dual compression procedure that reduces the bond dimension of these targets while uniformly preserving their overlaps with all bounded-bond comparators, with an error independent of system size. For matrix product states, this gives polynomial copy complexity in the system size, local dimension, bond dimension, and $1/\varepsilon$, together with polynomial runtime in the system size for fixed local dimension, bond dimension, and accuracy. The same framework yields proper agnostic learning of tree tensor networks on bounded-degree trees, with both copy complexity and runtime polynomial in the system size when the remaining parameters are fixed.

The topological order of the Kitaev toric code is insensitive to disorder in its couplings since all star and plaquette operators commute; consequently, the stabilizer ground-state manifold is independent of the individual coupling strengths, and the phase remains stable against weak local perturbations. This insensitivity, however, is a property of the eigenstates and not of the dynamics they generate, and we show that the disorder sensitivity of a probe prepared outside that eigenbasis can be a metrological resource. In particular, we investigate the estimation of the strength of three topological-order-breaking perturbations, the nonlinear Castelnovo-Chamon deformation, nearest-neighbor Ising interactions, and a magnetic field along horizontal edges, encoded on an initially separable probe through unitary evolution under the disordered toric code Hamiltonian. We demonstrate that the quenched average quantum Fisher information (QFI), a figure of merit for metrological precision, exceeds that of its ordered counterpart in suitable regimes of perturbation strength and encoding time. For the ordered case, we further identify optimal product probes, for which the quadratic and cubic terms of the short-time expansion vanish identically, leaving a transient quartic scaling of QFI. Interestingly, this window persists as long as the multipartite entanglement generated by the encoding continues to increase, and it survives under local dephasing, bit-flip, and amplitude damping noise acting independently on each site, with the non-unital channel being the least detrimental.

Circuit cutting enables quantum computations to be decomposed into smaller subcircuits at the cost of additional sampling overhead. Gate-cutting provides one such approach by replacing nonlocal gates with quasiprobability decompositions of local operations. Starting from the known optimal two-qubit gate-cutting formula, we derive complete sharp lower and upper envelopes relating the quasiprobability extent $γ$ to five established descriptors: entangling power, gate typicality, operator entanglement, Schmidt strength, and maximum product-input concurrence. We recast $γ$ as a Rényi-$1/2$ functional of the operator-Schmidt spectrum and show how the physical constraints on two-qubit spectra sharpen generic entropy bounds and select a small set of recurring extremal Cartan families. None of the five descriptors generically determines $γ$ alone, but each imposes exact constraints, revealing how substantially the optimal gate-cutting cost can vary between gates with similar nonlocal characteristics.

A longstanding open question in Boolean function complexity asks whether approximate degree composes multiplicatively under block composition. Although a general multiplicative upper bound is known, matching lower bounds have previously been established only for restricted classes of functions. We resolve this question for all total Boolean functions by proving the matching lower bound. Together with Sherstov's upper bound, our result shows that, for every pair of total Boolean functions $f:\{0,1\}^n\to\{0,1\}$ and $g:\{0,1\}^m\to\{0,1\}$, \[ \widetilde{deg}(f\circ g) = Θ\!\left( \widetilde{deg}(f)\,\widetilde{deg}(g) \right), \] where $\widetilde{deg}$ denotes constant-error approximate degree.

Population inversion and collective relaxation can both enhance the performance of a quantum heat engine, but through distinct mechanisms. We study a quantum Otto engine whose working medium is a symmetric collective spin of $N$ two-level constituents. For commuting work strokes and collective reservoir coupling, the dynamics reduces exactly to a finite birth--death process on the Dicke ladder, allowing a unified treatment of stationary operation, work fluctuations, and finite-time relaxation. In the complete-reset limit, passive work per cycle saturates with system size, whereas population inversion yields work that grows linearly with $N$. The work reliability shows the same linear scaling, exceeding the square-root behavior of $N$ independent engines. This enhancement originates from a macroscopic polarization displacement between hot and cold states, while collective coupling instead accelerates the finite-time dynamics through Dicke transition rates. For matched passive and inverted hot states, the extra gross work equals the Otto efficiency times the ergotropy of the inverted state. Charging the corresponding reversible excess state-formation cost removes this advantage, showing that the enhanced output converts a pre-existing active-state resource rather than generating a free thermodynamic gain. Exact finite-contact trajectory statistics further quantify how collective kinetics, fluctuations, correlations, and resource accounting remain linked away from complete reset.

We study how Clifford interactions with a fixed environment determine quantum transmission, in a setting that extends positive discrete quantum convolution . We characterize when Clifford operations on the environment can be replaced by operations on the signal input and the two outputs, and classify the interactions under local Clifford transformations . For pure stabilizer environments, we determine the noiseless, dephasing, and completely depolarizing parts of the channel directly from the interaction and environmental stabilizers, obtaining its quantum and private capacities . This reveals a distinction between interactions: those locally equivalent to positive convolution produce entanglement-breaking channels for every pure stabilizer environment, whereas every other interaction in the class admits noiseless quantum transmission with a suitable pure stabilizer environment . For positive convolution, environmental Clifford transport also allows us to separate the stabilized coordinates of an arbitrary mixed environment . These coordinates carry only a classical label shared by the receiver and environment, so removing them preserves quantum and private capacities . The resulting channel reduction yields a private-capacity bound by the modified relative entropy of magic of the environmental state .

High Performance Computing (HPC) and Quantum Computing (QC) systems are increasingly converging towards unified High Performance Computing-Quantum Computing (HPCQC) infrastructures, driven by a growing need to bridge classical and quantum workflows, which affects all levels of the system stack, from the hardware to compilers and runtimes, all the way to applications. However, today's QC devices are still in the Noisy Intermediate-Scale Quantum (NISQ) era, are error-prone and resource-limited, and therefore require specialized optimizations and topology mappings to achieve sufficient fidelity. This places special emphasis on proper compilation and optimization within the overall quantum software stack. Many existing stacks remain fragmented, with separate components responsible for device selection, compiler-pass optimization, and job queue scheduling. This paper proposes a unified, learning-based selector that integrates these disparate stages into a cohesive framework. Our proposed selector scheme leverages reinforcement learning and deep learning models that can be extended to simultaneously optimize multiple objectives -- such as fidelity, compilation time, and scheduling latency -- while dynamically adapting to circuit characteristics and device conditions.

We introduce a class of tensor-network states in which physical legs are shared among local tensors, termed leg-tied tensor ansätze (LETTA). Physical leg ties encode long-range correlations directly, while a virtual matrix product state (MPS) backbone retains short-range multipartite entanglement. The linear virtual backbone allows us to develop a deterministic density matrix renormalization group-like variational optimization algorithm using exact contractions over the active tie-boundary sets and local minimization. We demonstrate the advantages of LETTA for the two-dimensional frustrated $J_1$--$J_2$ Heisenberg model and the three-dimensional transverse-field Ising model. Our results show that LETTA is substantially more accurate than same-bond-dimension MPS calculations and can typically reach the accuracy of much larger MPS calculations using one order of magnitude fewer variational parameters. LETTA thus opens the door for explicitly correlated tensor-network states that can encode long-range correlation beyond virtual bonds.

Reducing the qubit overhead of quantum error correction is a central challenge for scalable fault-tolerant quantum computing. Recent ultra-high-rate quantum codes offer a promising route toward this goal, with some constructions requiring as few as two physical data qubits per logical qubit. However, systematic principles for navigating the tradeoffs among encoding rate, distance, check weight, and blocklength remain lacking. Here, we develop and analyze principles for exploring this design space, and use them to design compact code constructions with improved performance. We develop code templates based on a pair-partition construction and a halving transformation that further reduces blocklength. Motivated by ensemble analysis of the degree distributions, we identify column weight as a key design parameter: increasing the column weight enables larger distances at compact blocklengths, at the cost of heavier checks. We find that at physical error rates of 0.1%, the benefits of increased distance often outweigh the penalty associated with heavier checks. Applying this framework, we identify numerous compact codes with favorable parameters, including [[90,21,11]], [[140,31,15]], and [[200,43,20]] non-CSS codes with check weight 10. Moreover, we develop symmetry-informed strategies for identifying low-weight logical bases. These results provide systematic strategies for designing ultra-high-rate quantum codes and navigating their Pareto frontier.

For normal PEPS, the fundamental theorem settles at the finite level whether virtual-bond gauge exhausts a tensor network's representation freedom. We ask the first-order question at a fixed representation, from both sides of the differential: which tensor variations leave the state unchanged without being bond gauges, and which physical directions can no variation reach? We answer both exactly for weighted graph state (WGS) tensor networks with equal physical and bond dimension $q\ge2$, which include the graph-state resources of measurement-based quantum computation. Dividing a single-tensor variation by the nonvanishing amplitude turns it into an arbitrary function on the closed neighborhood of its vertex. Overlapping neighborhoods give the complete kernel. Its non-bond part is generated on periodic regular-polygon tilings by triangles, chordless squares, and edge-sharing diamonds. Under stated period conditions, generic gauge completeness on all thirty-nine families studied identifies this nullity as a WGS rank drop: for thirty-three families at every $q\ge2$, and for six at $q=2$. Supports outside every neighborhood give the missing directions: at qubit graph states on the eleven Archimedean tilings every nearest-neighbor $XX$ and $YY$ direction is missing, including on honeycomb, where the non-bond kernel is empty. On large honeycomb and square tori, small nonzero coherent $XX$ errors leave the bond-two PEPS set on the same graph. Removing redundant parameters and supplying missing directions are therefore distinct operations.

Constructing optimal quantum information protocols without complete knowledge of the underlying states or channels is a central challenge. We address this challenge by developing universal correlation detection as a common building block for quantum communication. Our detectors distinguish a bipartite state from the product of its marginals and attain the same first-order asymptotic performance as optimal tests constructed with complete state information. For general bipartite quantum states, knowledge of a single marginal suffices: a detector depending only on that marginal is first-order optimal for every compatible state. For classical-quantum states, the detector is fully universal and requires no prior state information. By combining these detectors with position-based decoding and convex splitting, we construct channel-independent coding schemes that achieve capacity for a range of communication tasks. These results turn universal correlation detection into a systematic tool for universal protocol design, providing a unified route to designing capacity-achieving protocols for many communication tasks over unknown quantum channels.

The advent of pseudoentanglement and computational entanglement theory bootstrapped a wave of research at the intersection of computer science and information theory. In parallel, computational cryptography has undergone substantial development, prompted by the introduction of pseudorandom states and followed by the establishment of a baseline for the computational hardness required for quantum cryptography, from which EFI pairs emerge as a central primitive. We study the connection between pseudoentanglement and computational cryptography through EFI pairs. Our goal is to enable the use of resources arising from computational entanglement theory in the field of cryptography. For this, we establish the relation between operational instances of pseudoentanglement and the hierarchy of minimal assumptions for computational cryptography. We show that the existence of pseudoentanglement under two different operational definitions, with efficient state generation, is a sufficient condition for the existence of EFI pairs. Combined with a previously established result that the converse also holds under the second definition, this allows us to also demonstrate their equivalence. This places pseudoentanglement alongside other minimal assumptions in cryptography, not only offering an alternative perspective on this fundamental problem, but also building a bridge that allows insights from either area to inform the other. While proving these theorems, we introduce and demonstrate technical lemmas in quantum information and computational entanglement theory, relating the computational entanglement measures to the distance between states, establishing distinguishing conditions for mixtures of two families given pairwise distances between their states, and demonstrating the first continuity relation for a computational entanglement measure.

Non-Clifford gates are essential for universal quantum computation, yet implementing them fault-tolerantly remains a central challenge for stabilizer codes. Here, we show how a syndrome degree of freedom can mediate a logical non-Clifford gate. Releasing one stabilizer check makes an additional logical qubit available within the encoded data block. Two Pauli rotations, followed by syndrome measurement and Clifford feed-forward, then implement a deterministic logical $T$ gate on every stabilizer code of distance at least two, in a suitable logical basis. During the ideal rotations, the state remains in an intermediate stabilizer code whose distance we determine exactly. For pure codes with a balanced factorization, this distance grows with the original code distance, whereas the maximum weight of the stabilizer generators bounds the intermediate distance from above. We realize the mechanism in two circuits that tolerate a single fault under local stochastic circuit noise: a fixed 22-qubit construction admitting recursive error suppression and a direct Golay-code gate protected by measuring a stabilizer check transported through the non-Clifford rotation, which can recover the unknown encoded state even after rejection. Serial implementations with ancilla reuse, reset, and flexible two-qubit connectivity require at most 33 and 32 physical qubits, respectively. These results establish a general mechanism for logical non-Clifford gates and demonstrate how syndrome measurements and recovery can protect the intermediate evolution of encoded information.

We show that the regularized channel Rényi divergence is continuous at $α= 1$. As consequences, we establish an exponentially strong converse for channel discrimination, a subchannel-smoothed asymptotic equipartition property, a relative entropy accumulation theorem, and a new proof of the generalized quantum Stein's lemma. Our result further shows that the regularized channel relative entropy is computable. The continuity proof relies on a variational formula that expresses the regularized channel divergence as a single-letter optimization over variables of unrestricted finite dimension. We then establish continuity using a novel spectral confinement technique.

Temporary occupation of qutrit levels can reduce the width and depth required for binary circuit logic in quantum computing. We introduce an efficient intermediate-qutrit decomposition of multi-controlled Toffoli gates with binary-subspace inputs and outputs. For balanced control widths $n=2^h-1$, the proposed decomposition is evaluated hierarchically through a tree, allowing independent subtree computations to proceed in parallel and reducing the depth from linear to logarithmic. The balanced low-depth construction requires $6n+3$ logical $P_9$ injections and $\frac{n-3}{4}$ clean ancillary qutrits. It matches the direct $P_9$ count of a recursively extended Clifford+$P_9$ baseline derived from the state-of-the-art work while using asymptotically one-quarter as many clean ancillas and replacing linear depth with logarithmic depth. For arbitrary control widths, a sequential extension preserves the $6n+3$ $P_9$ count but has depth $O(\log m+n-m)$ for a balanced core $m=2^h-1\leq n$, which is linear in the worst case over $n$. By reducing the resource overhead of a widely used reversible primitive, the proposed decomposition provides a practical building block for the design and compilation of more resource-efficient quantum algorithms in the fault-tolerant regime.

Avoided crossings in the correlated many-body spectrum play a central role in determining the conditions for adiabatic state preparation in interacting quantum systems. We investigate this connection in finite spin-boson systems by combining exact diagonalization of the many-body spectrum with time-dependent simulations of adiabatic switching protocols. By comparing the adiabatically prepared state with the exact ground state, we determine the switching times required for reliable preparation as a function of the spin-boson coupling strength and bosonic mode structure. We show that regions of small many-body level spacings, associated with avoided crossings, impose the strongest constraints on adiabatic preparation and explain the observed dependence of the required switching times on the interaction strength. Furthermore, while the ground-state energy follows the overall spectral trends, local observables such as Pauli matrix expectation values exhibit additional non-monotonic behavior arising from coherent oscillations in finite systems. These findings can provide concrete benchmarks for both the theoretical treatment of open quantum systems and practical implementations in quantum simulation and qubit control.

This paper sets out a computational workflow that reconstructs the phylogeny of human Y-chromosome populations from a Variant Call Format (VCF) file of biallelic Single Nucleotide Polymorphisms (SNP). The two classical phylogenetic decisions - topology selection and root placement - are cast as Quadratic Unconstrained Binary Optimisation (QUBO) problems. The workflow combines two QUBO formulations with an Alternating Direction Method of Multipliers (ADMM) decomposition strategy and a plug-in Digitized Counter-Diabatic Quantum Optimization (DCQO) solver, enabling large phylogenetic optimization problems to be executed across multiple classical or quantum computing resources. The DCQO gate-based optimizer drives each ADMM-block QUBO with short-depth counter-diabatic circuits in the impulse regime, without the necessity for an outer variational loop. The combination of ADMM decomposition and the DCQO block solver facilitates problem sizes that surpass the qubit budget of any individual digital quantum processing unit call, while maintaining the integrity of the original objective. The workflow extracts genotype information from VCF files, reconstructs topology and rooting through two QUBO formulations, and annotates the resulting tree using PhyloTree. The resultant data set comprises a Nexus-annotated rooted tree, in addition to diagnostic figures. The workflow demonstrates the potential of modest-scale QUBO formulations combined with ADMM decomposition to serve as a scalable alternative to greedy heuristics in the domain of population genomics.

Autocorrelation functions play a key role in the theoretical characterization of the dynamical properties of interacting many-body quantum systems. Recently, bringing together the eigenstate thermalization hypothesis and hydrodynamics, it was theoretically predicted that the relaxation of autocorrelators can be described by the \textit{relaxation-overlap inequality}, which, when saturated, predicts a hierarchy of relaxation exponents for a set of operators that are easily identified and constructed. Here, we employ a trapped-ion quantum simulator to experimentally demonstrate it in the diffusive regime; to do so, we have extended the theory of the overlap-relaxation inequality to systems with multiple conservation laws. Our study thus opens the path to a thorough characterization of the relaxation to equilibrium and appearance of hydrodynamic behavior in quantum matter.

Distributed quantum computation requires many entangled pairs to be available simultaneously, so routing must optimize fidelity from a fixed, short-lived set of network resources rather than the rate of pairs accumulated over time. We formulate this one-shot routing problem for heterogeneous Werner-state links and jointly optimize path selection and the schedule of entanglement swapping and distillation. We show that the common purify-then-swap ordering is not optimal network-wide and that exact schedule enumeration requires $m^{Θ(m)}$ time. We introduce Fidelity-Optimizing Local Detours (FOLD), a heuristic that starts from the highest-fidelity path and merges a detour only when distillation improves on both routes and raises end-to-end fidelity. FOLD runs in polynomial time, recovers almost all of the optimal fidelity on tractable instances, and is four orders of magnitude faster than exact optimization at circuit rank $5$. On the Internet topologies where any strategy improves on shortest-path routing, FOLD achieves the highest mean end-to-end fidelity among the polynomial baselines. We further extend the formulation to links whose fidelities are known only as distributions, where uncertainty, rather than the effort spent routing, limits the fidelity delivered. Through an example of requests competing for the same links, we show that coordination becomes a condition for feasibility, and that a shared path budget controls the fidelity trade-off between them.

At cryogenic temperatures, organic single-photon sources (SPSs) offer Fourier-limited emission, virtually unlimited photostability, and emission wavelengths selectable by molecular design, making them attractive for quantum metrology, secure communication, and photonic quantum information processing. However, their efficient integration with photonic microstructures has remained challenging, limiting photon collection from single organic emitters under cryogenic operation. Here, we demonstrate a cryogenic planar metallo-dielectric antenna that efficiently directs the emission of a single dibenzoterrylene (DBT) molecule towards the collection optics. The device reaches a collection efficiency of 97% and delivers 100 million photons per second into the first lens. We measure a photon indistinguishability for the Fourier-limited transition of 91.2% while maintaining a high single-photon purity of 97.7% under strong continuous-wave (CW) and pulsed excitation. These results establish organic molecules as a high-performance platform for single-photon generation and represent an important step towards scalable organic quantum photonic technologies.

Randomized measurement protocols give experimental access to low-degree polynomial invariants of a quantum state rather than to the state itself, which raises the question of what the best entanglement criterion is that can be built from finitely many such invariants. In this work we answer this question through convex duality. For each degree we introduce the cone of local unitary trace inequalities that are valid for separable bipartite states in all local dimensions, together with its one-matrix counterparts for Hermitian and positive semidefinite matrices. Each cone is the polar dual of a moment cone; we also determine the minimal combinatorial parametrization of the separable cone. The framework organizes the known moment criteria: the PPT criterion using the first three moments of the partial transposition is the image under an embedding of a Hankel determinant from the positive semidefinite cone to the bipartite cone, which we show to be an extremal ray, and we determine the first nontrivial separable cone completely, finding exactly four extremal rays. The framework allows us to analyze the realignment criterion and its centered (or enhanced) variant. We prove that the even singular value moments of the (centered) realignment matrix are trace invariants, associated with explicit fixed-point-free involutions. Extracting the optimal trace-norm bound from $m$ such moments thus becomes a dimension-free truncated moment problem, which we solve in closed form for $m = 2$ and relax to a semidefinite program of size $O(m)$ for arbitrary $m$. The dual solutions are polynomial minorants of $\sqrt{x}$ on $[0,1]$, and two explicit families, binomial and $L^1$-weighted, yield hierarchies of separability inequalities. Finally, we compare the criteria against one another and on PPT entangled states.

Quantum heat transport governs energy exchange processes and statistical laws in non-equilibrium quantum systems, and plays a pivotal role in quantum thermodynamics. We investigate the steady-state thermal transport of a noncommuting coupled spin system. We employ the quantum dressed master equation approach within the framework of open quantum system theory to accurately analyze the non-equilibrium dynamics, ensuring the validity of transport results in the strong coupling regime. Our results demonstrate that noncommuting spin coupling serves as a significant resource for modulating the nonlinearity of the heat current. Specifically, in the weak spin-coupling regime, the system exhibits robust negative differential thermal conductance (NDTC) across various spin numbers. By deriving analytical expressions for the heat current in both the single-spin and large-spin limits, we reveal that this NDTC behavior is governed by microscopic cycle fluxes. Physically, this arises because spin excitation channels induced by the cold reservoir are suppressed under a large temperature bias, thereby blocking energy exchange cycles. Conversely, in the strong spin-coupling and large temperature bias regime, the quantum system demonstrates pronounced thermal rectification. This high rectification efficiency originates from the unidirectional saturation of the heat current, rendering the system a promising candidate for high-performance thermal diodes. Furthermore, we extend the model to a three-terminal configuration to construct a quantum thermal transistor. By manipulating the temperature of the gate reservoir, we achieve efficient modulation and amplification of heat flow between the source and drain. The heat amplification factor is shown to far exceed unity in specific operating regions, confirming significant thermal amplification.

Quantum circuit optimization is critical for mitigating the noise inherent in current quantum hardware. Quantum compilers typically sequentially apply multiple optimizations (also called ``optimization passes'') to improve the circuit. The impact of the order in which these passes are executed has yet been largely unexplored. This paper investigates the significance of the order of optimization passes within quantum circuit compilation, specifically analyzing interactions between different optimization methods and quantifying their mutual influences. Using Qiskit's compiler, we systematically evaluate pairwise combinations of 16 selected optimization passes, measuring circuit depth and gate count across various benchmark circuits. Our findings indicate dependencies between certain optimization passes, demonstrating that the order of the passes affects the optimization quality. In some cases, the worse performing sequence can be corrected through repeated pass application. %such that they are as good as the best performing one by extending the sequence. Experiments on multi-pass sequences show that more than two optimization passes may have an impact on each other but that this always links to the previously found pairwise effects. We observe that it is important to initially choose the best order of optimization passes to get the best possible optimization for the given circuit. The experiments reveal some factors which are important to choose the best, or at least a good, order; among those, the resulting optimization sequence depends the most on the native gate set.

Phase-space representations reveal the geometry of quantum mechanics and distinguish quantum features from classical ones. However, the positivity of a density operator is among the properties of quantum states that phase-space representations capture least directly: deciding whether a phase-space function describes a physical quantum state has so far required global conditions coupling distant points in phase space. Here we show that these conditions can in fact be made local, by considering the Husimi representation in phase space. We establish a complete set of conditions which captures when a phase-space function $f$ is the Husimi function of a quantum state, with each condition involving only the derivatives of the function $f$ evaluated at a single phase-space point. We further show that each condition has an equivalent algebraic characterization, which takes the form of the nonnegativity of a determinant of the underlying operator in a displaced Fock basis. As a result, these conditions obey a recurrence relation organizing them into a differential hierarchy, which terminates based on the rank of the operator. Our results thus show that operator rank and positivity are local properties in phase space, reinforcing the role of phase-space representations as a geometric description of quantum mechanics.

We reveal that the information geometry of entropy production exhibits an intrinsic anisotropy, providing a unified origin for the inequivalent geometric constraints obeyed by its different components. Using a hierarchical projection structure of quantum relative entropy, we derive an exact orthogonal decomposition of entropy production into three distinct geometric contributions associated with the deviation of the Gibbs projection temperature from the reference temperature, the deviation of the environment from its Gibbs projection state, and system--environment correlations. We demonstrate that these contributions obey fundamentally different geometric bounds: the first reduces to a classical Kullback--Leibler divergence and admits no universal upper bound in terms of the trace distance and the system and environment dimensions alone, whereas the latter two admit rigorous distance-based bounds with dimension-dependent factors. The framework also applies to classical Markovian dynamics described solely in terms of the system state, for which the system--environment correlation contribution is absent from the decomposition. Combining this geometric decomposition with dynamical speed limits, we obtain rigorous bounds on entropy production expressed solely in terms of physically accessible quantities, such as the mean energy and Hamiltonian variance.

A quantum measurement transforms a quantum statistical experiment into a classical one, but different measurements generally yield experiments with different statistical information. We introduce quantum-to-classical sufficiency: relative to a prescribed measurement class, a measurement is sufficient if its induced classical experiment Blackwell-dominates those from every other measurement in the class. This separates two components of quantum inference: reducing the measurement class through symmetry or decision-theoretic arguments, and identifying a canonical measurement in the reduced class by an experiment-level sufficiency condition. We establish a factorization criterion where the parameter enters the group-averaged experiment only through weights of an orthogonal block decomposition. The block-label measurement is then sufficient relative to all invariant measurements. For tensor-product models under unitary conjugation, this identifies weak Schur sampling as the sufficient measurement for spectral inference. Combined with risk-preserving symmetrization, it reduces invariant Bayes and minimax problems over all measurements exactly to classical decision problems based on Young diagrams. We derive sharp first-order asymptotic Bayes and minimax risks for smooth spectral functionals. We establish an analogous reduction for a noncompact group action in a continuous-variable setting. We consider displaced thermal states and functionals of the thermal parameter with an unknown displacement. Within displacement-invariant measurements, total residual photon number measurement emerges as the sufficient measurement. Combined with Hunt-Stein reduction, this yields exact finite-sample reductions of Bayes-minimax and minimax problems over all measurements to classical decision problems based on the total residual photon count, which follows a negative binomial distribution.

Dynamical simulation of quantum many-body systems is a central task in quantum chemistry and requires efficient wavefunction representations. Although tensor-network and neural-network quantum states have achieved considerable success in ground-state calculations, entanglement growth hinders their application to quantum dynamics. Quantum computing may offer a route to quantum advantage, but algorithms such as Trotterization generally require fault-tolerant quantum computers, whereas near-term hardware supports only limited circuit sizes. Variational quantum simulation (VQS) instead represents the evolving state with a single shallow, fixed-size parameterized quantum circuit (PQC). Here, we introduce nonorthogonal variational quantum simulation (NOVQS), which applies linear combinations of parameterized quantum states to real- and imaginary-time evolutions. We design a shallow, hardware-friendly ansatz tailored to second-quantized electronic-structure Hamiltonians, together with resource-efficient protocols for measuring the matrices and vectors in the parameter equations of motion. Error analysis and resource estimation are also provided. Numerical simulations of hydrogen chains and the nitrogen molecule demonstrate that a collection of shallow, or even single-layer, PQCs can match or outperform a much deeper PQC in VQS. In particular, we identify a trade-off between circuit number and depth. NOVQS therefore provides a flexible route to enhancing wavefunction expressivity under circuit-depth constraints, making it a promising framework for quantum dynamics simulations on near-term quantum processors.

Hybrid quantum-classical compilers exchange programs among circuit, control-flow, pulse, device, and physical representations. Existing formats make different abstraction choices, so the properties that must survive a lowering step are often enforced by tool-specific code rather than stated in a common intermediate representation (IR). We present QaiJi IR, an eight-layer family organized by a \emph{five-axis semantic contract} for data, semantics, lowering, runtime, and verification. Its L4 SemanticIR records the operation class, declared equivalence level, optimization role, and classical-feedback model as attributes, and maps operation classes to ISA-neutral hardware actions. The prototype provides typed quantum and classical circuit nodes, OpenQASM~2 compatibility input, canonical OpenQASM~3 output, explicit rejection of unsupported constructs, and executable gate-convention checks. A representative measurement-conditioned program reaches a canonical QASM fixed point, acquires a measurement-to-condition edge, passes an exact aggregate consistency check, and produces a symbolic pulse template. For a one-bit active-reset case, device lowering materializes ALU/FPROC records and a conditional branch. Running the resulting virtual pulse processing unit (VPPU) program with externally supplied outcomes 0 and 1 respectively skips and executes the conditional drive. These tests validate the represented compiler path and binary branch behavior. They do not establish a physical feedback loop, because the simulator cannot yet apply mid-circuit measurement collapse and continue the same dynamical trajectory.

True random number generation is a critical capability for fault-tolerant quantum computing at millikelvin temperatures. Yet existing Josephson-junction-based TRNGs all rest on a widely accepted but untested assumption: that reliable entropy extraction requires precisely controlled device parameters. Here we show that this assumption does not always hold. We demonstrate a counterintuitive finding: a single current-biased Josephson junction, regardless of its parameter quality, can serve as a cryptographic-grade true random number generator. To establish the universality of this conclusion, we deliberately selected the most extremely deviated devices from fabrication, with critical currents three orders of magnitude away from theoretical predictions and $I_cR$ products an order of magnitude above conventional values, as the ultimate stress test. Even under these extreme conditions, the raw Shannon entropy reaches 0.9981~bit (99.8\% of the theoretical maximum), with a min-entropy of 0.9271~bit. Using a square-wave pulsed-bias scheme, we tune the switching probability to $P\approx0.5$. After SHA-256 post-processing, the bitstreams pass all 15 NIST SP 800-22 tests under a conservative $m=3$ criterion that is more demanding than the standard recommendation, and this certification holds across the entire 100-700~mK operating window of a dilution refrigerator.

Magic-state cultivation offers a promising alternative for lowering the cost of non-Clifford operations in fault-tolerant quantum computing (FTQC). However, realizing cultivation in practice exposes two challenges: (i) the lack of an open-source classical runtime layer between logical software and physical control, and (ii) the latency constraints on protocol-specific decisions that determine magic-state readiness. To address these challenges, we adopt an algorithm--hardware co-design approach. At the algorithm level, we develop a two-stage early-escape scheme that identifies an informative subset of detectors offline, constructs a compact decoding problem, and performs partial decoding in parallel with complete decoding at runtime, allowing high-confidence attempts to advance before full decoding completes. At the hardware level, we present MagiCFirm, a configurable runtime that combines offline-compiled microprograms with dedicated datapaths for detector construction, event processing, and protocol control, enabling end-to-end execution of magic-state cultivation. Across evaluated configurations, MagiCFirm reduces wall-clock magic-state preparation time by up to 39.3% at matched logical error rate. For a representative magic-state-bound workload, this translates to an estimated 11% reduction in overall application runtime.

A distinction should be made between quantum uncertainty relations and the broader uncertainty principle. The former are precise statistical consequences of quantum mechanics; the latter, when interpreted as excluding simultaneously definite conjugate variables and particle trajectories, is an additional ontological claim not implied by the uncertainty relations themselves. We examine this distinction using Feynman paths, Nelson's stochastic mechanics, Bohmian mechanics, and finite-speed persistent Kac dynamics. Feynman paths exhibit Brownian-like short-time scaling, while Nelson derives Schrödinger dynamics from Wiener diffusion supplemented by dynamical assumptions. Bohmian mechanics, by contrast, reproduces quantum predictions while retaining definite particle trajectories. Kac dynamics provides continuous, piecewise differentiable finite-speed trajectories whose diffusive limit approaches Wiener kinematics. Moreover, after an appropriate Wick rotation, its coupled two-sector transport equations can be mapped to the Dirac equation. These examples demonstrate that the experimentally established uncertainty relations are compatible with markedly different underlying path structures. They therefore do not, by themselves, rule out a microscopic trajectory description of quantum dynamics.

Random matrix spectral statistics are widely used to diagnose quantum chaos in open systems, but whether chaotic eigenvalue correlations are accompanied by Haar-typical eigenoperators remains unclear. We study the operator-entanglement statistics of Liouvillian eigenoperators with near-maximal entanglement, analogous to states near the middle of the spectrum in Hamiltonian systems. Using the Kullback-Leibler divergence, we show that Haar-random statistics accurately describe both the Ginibre and class-AI$^\dagger$ Gaussian ensembles. For purely dissipative random Lindbladians, we find that locality of the jump operators drastically alters the eigenoperator-entanglement statistics. Nonlocal Lindbladians remain relatively close to Haar-random behavior, whereas local Lindbladians deviate increasingly from random-matrix statistics with system size. Moreover, unlike in Hamiltonian systems, the most highly entangled eigenoperators of local Lindbladians do not generally lie in the region of largest density of states, owing to the clustered structure of the complex eigenspectrum. We introduce an iterative $σ$-clipping scheme to extract the high-entanglement distribution without preselecting a spectral window, and find that it is Gaussian for nonlocal Lindbladians but log-normal for local ones. Remarkably, the same log-normal distribution, with no additional fitting, also describes dissipative mixed-field Ising chains belonging to distinct non-Hermitian symmetry classes. Our results therefore point to a universal eigenoperator-entanglement distribution for local Lindbladians that is not captured by generic non-Hermitian random-matrix ensembles.

Fault-tolerant compilation can disperse high-level structure: schedules split an accumulated phase across rounds, gate synthesis replaces an angle by a Clifford+$T$ word, and randomized compiling spreads rotations over sign-randomized fragments. They preserve the computation but change how cheaply a downstream compiler can recover the aggregate phase data. We formalize this representation-dependent recoverability by charging two channels: output committed before the suffix arrives, and a serialized restart state crossing the cut. For an $r$-round accumulation of a commuting layer with $m$ generators at accuracy $ε$ ($K_ε=Θ(1/ε)$), any $p$-pass compiler correct on every valid stream with failure probability at most $δ$ obeys $\overline{A}_p+(2p-1)S\geq(1-δ)m\log_2 K_ε-h_2(δ)$, where $\overline{A}_p$ is committed output and $S$ is the crossing-state cap. The bound covers compile-time randomized compiling; a memory-capped block compiler attains it within a constant factor, and direct semantic aggregation reaches compact output with logarithmic state. The two channels are not always interchangeable. A compiler whose committed prefix is executed at the cut pays a toll the state channel never pays: the entropy $\log_2\binom{m}{k}$ of the mask naming which $k$ coordinates it commits early. Compilers that defer or buffer pay none of it. We prove both directions and, with instrumented compilers under a preregistered protocol, measure a per-generator toll matching $\log_2\binom{m}{k}/k$ that vanishes for a public mask and a buffered control. Under a disclosed fixed-total-error Clifford+$T$ and surface-code model, a materialize-first pipeline costs orders of magnitude more logical $T$ states and spacetime volume than a semantic-first one. Phase semantics should therefore be preserved until aggregation whenever the interface permits.

We study the roles of broken spectra and exceptional points in finite-time driven non-Hermitian fermionic dynamics. We compute the Nambu biorthogonal correlation matrix for this purpose. The imbalanced-pairing Kitaev chain serves as our concrete realization. Transient passage through a broken-spectrum region amplifies preparation memory. The effect survives when the final Hamiltonian returns to a real-spectrum regime. Negative imbalance forces spectral nonpositivity in the static endpoint state. We isolate the genuine drive history by subtracting out this baseline, leaving an excess that is strictly controlled by the accumulated imaginary-energy action and persists over the entire post-ramp time window. A connected longitudinal correlation mirrors this physics. Its slow-ramp growth tracks the corresponding doubled action. Unstable sectors instead continue amplifying post-ramp if the drive halts inside the broken-spectrum region. Exceptional points yield distinct physics. The finite-time propagator and subsystem correlation matrix remain entirely regular near an exceptional endpoint, even as the quasiparticle gap exhibits its characteristic square-root closing. This finite-time regularity reflects the analyticity of the matrix evolution in the endpoint parameter; a diagonalizable endpoint is strictly not required. A diverging long-time crossover eventually reveals the exceptional scale. We halt the drive exactly at the exceptional point to find that the correlation projector and the connected longitudinal correlation share an identical ballisti front. The subsystem saturation length establishes a distinct but comparable spatial scale. Memory and exceptional-endpoint scalings show no divergence across the tested negative-imbalance range. Memory scaling is fixed by the drive and remains insensitive to the specific choice of real-spectrum final endpoint.

Variational quantum algorithm is a leading approach for quantum chemistry and many-body physics on noisy intermediate-scale quantum devices. The performance depends strongly on the structure of the parameterized quantum circuits. Quantum architecture search (QAS) can automate ansatz design. However, it requires repeated training and evaluation of many candidate circuits, leading to high evaluation cost. In this work, we propose a noise-aware quantum architecture search framework based on ZX-calculus topological reuse (ZX-QAS). The framework encodes the search space with a ternary Gray-code mapping and integrates a noise-aware quantum neural network with a ZX-calculus topological reuse mechanism. The effectiveness of the framework is validated through ground-state energy estimation tasks and one-dimensional transverse-field Ising model tasks under noisy conditions. The results show that the ZX-QAS exhibits stable convergence and remarkably reduces the cost of expensive evaluations under noisy conditions.

Quantum error-correcting decoders provide both corrections and confidence estimates for the logical-error risk of individual measurement records. Such confidence can guide postselection, but it depends on the accuracy of the decoder noise model. When the physical device drifts away from that model, confidence measures such as the logical gap can become miscalibrated. We show that this mismatch can itself provide useful information. On IBM quantum hardware, syndrome statistics drift across consecutive acquisition windows, and the resulting detector histories differ substantially from those predicted by the stationary detector error model used for decoding. We observe a similar hardware-model mismatch in independent Google surface-code memory data. We exploit this effect by assigning additional rejection weight to detector histories that are unlikely under the assumed model. For minimum-weight perfect matching (MWPM), the minimum weight $W$ provides an inexpensive proxy for syndrome surprisal. On held-out IBM repetition-code memories, likelihood-aware postselection reduces the retained logical-error probability (LEP) by $10.6\%$ at $d=7$ and $28.8\%$ at $d=9$, both at $15\%$ rejection. On Google ten-round $d=5$ XZZX surface-code memory data, it reduces retained LEP by $75.4\%$ at $90\%$ rejection. Applied to Google's magic-state cultivation experiment with the Tesseract decoder, it reduces tomography infidelity by $34.7\%$ with $30\%$ additional grafting-stage rejection, or increases accepted yield by $30.4\%$ at a target fidelity of $97.0\%$. Burst-noise simulations show that the advantage persists as code distance and syndrome-extraction volume increase. The method reuses quantities already produced during logical-gap decoding and requires only an additional fitting step.

The simulation of nonlinear ordinary differential equations on quantum computers is inherently challenging, as quantum gates are linear operators on qubit states. In this paper, we put forth a Koopman-von Neumann (KvN) operator based algorithm for solving nonlinear ordinary differential equations on a quantum computer which overcomes the innate limitations of quantum operations. In this approach, a Liouville probability density is embedded into a wavefunction, the evolution of which is governed by an operator dual to the Koopman operator. The trajectories corresponding to the nonlinear differential equations are reconstructed from the average value of Koopman observables evaluated through quantum measurements. We specifically evaluate the computational limitations of solving nonlinear equations within this Liouville embedding framework. An Ehrenfest-type estimate is derived that relates the reconstruction error to the covariance of the transported density, highlighting the competition between linear stretching and Hessian-induced folding.This leads to a key stability criterion, which depends on the local Ehrenfest-Reynolds number. We discuss the effects of measurement-induced errors including those due to Hadamard-test sampling, amplitude estimation, and bias due to covariance in probabilistic Grover-type inference on the evaluation of trajectories. The limiting bounds on the accuracy of quantum computations are numerically verified for the Lotka-Volterra system and for the quartic oscillator. We observe a rapid growth in computational errors when the Ehrenfest-Reynolds number approaches the predicted threshold. The bounds resulting from our analysis provide key guidelines for selecting the width of the initial Gaussian probability distribution associated with a system of nonlinear ordinary differential equations.

The dissipative transverse-field Ising (TFI) model provides a paradigmatic setting for nonequilibrium quantum many-body physics. We show that a class of boundary-driven TFI models subject to dissipation at only one boundary possesses hidden time-reversal symmetry, which enables an exact construction of their nonequilibrium steady states. The solution admits a matrix-product representation and defines a nonequilibrium partition function from which steady-state observables can be evaluated efficiently. We use the exact solution to characterize the microscopic structure of the steady state through its z-magnetization and two-point correlations. A striking feature is that the local field at the dissipative boundary governs the spatial organization of the steady state throughout the chain. The steady state typically exhibits boundary-localized magnetization profiles and exponentially decaying correlations, whose characteristic length scales are set by the dissipative boundary. In the weak-driving limit, suitably tuned boundary fields can reorganize the NESS into a delocalized single-interface structure, giving rise to long-range correlations that decay linearly with distance.

The compressed permutation oracle has been used to analyze the quantum security of a number of cryptographic constructions which resisted prior techniques. However, these analyses were fundamentally limited by the poor soundness of the method: the technique was proven sound only up to $O(N^{1/12})$ queries to permutations on $N$ elements. We revisit this analysis, improving the soundness bound to a tight $Ω(N^{1/2})$. In addition to being tighter, our proof is conceptually simpler and more direct, and gives the same bound in the ideal cipher model. The main technical idea is to construct the compression isometry from a simple POVM on the naive purification, a technique which may find wider applications. As immediate applications, our results yield tight, concrete collision and pre-image lower bounds for the sponge hash construction underlying SHA3 and the Davies--Meyer compression function used in SHA1 and SHA2. More broadly, the improved soundness theorem provides a general-purpose tool for analyzing quantum security in settings where random permutations or ideal ciphers serve as the underlying primitive.

We prove that constant-space-overhead fault-tolerant quantum computation can be achieved with provably strictly logarithmic time overhead, improving over the best known results with additional subpolylogarithmic factors. Our main construction uses polynomial-subrank transversal logical $\CCZ$ gates on good quantum locally testable codes to implement addressable universal computation by transferring batches of logical qubits between dense storage and active logical subspaces while reusing the same ancillary workspace. Logical $\CCZ$ gates are implemented directly by the transversal operation, so only stabilizer resource states require separate preparation. Furthermore, we give an alternative construction that also achieves purely logarithmic time overhead based on modifying the quantum Reed--Solomon magic-state distillation scheme of Nguyen and Pattison. Recursively applying a fixed distillation circuit protected by qLTCs of increasing block length eliminates the subpolylogarithmic time factor.

Quantum Reservoir Computing (QRC) exploits the rich dynamics of quantum many-body systems to process time-dependent information with high-dimensional state spaces. While neutral atom arrays offer a scalable platform for this paradigm, realizing intrinsic temporal memory without relying on external classical buffering requires precise control over the relaxation dynamics of the system. We address the necessity of specific non-unitary dynamics for enforcing fading memory while overcoming the lack of separability. This study simulates and empirically identifies the specific dynamical regimes required to maximize the computational capacity of the reservoir, addressing the amount of dissipation, the effectiveness of lying at the edge of quantum chaos, and that of time-multiplexing compared to the scaling of the physical size of the system. Here we show that controlled dissipation is strictly necessary to induce echo state property, fading memory, and separability, in neutral atom arrays. Computational performance increases at the edge of quantum chaos. The counter-intuitive residual memory provided by the unital phase damping channel is justified by introducing a model based on pure outputs. The consequent implementation enables the solution of complex non-linear tasks, such as the Mackey-Glass time series, with as few as $N=5$ atoms. We establish a rigorous framework for engineering dissipative quantum reservoirs required for intrinsic temporal processing on near-term quantum devices.

We determine the optimal universal coefficient in a reduction of multiple to binary quantum hypothesis testing. Specifically, for every finite ensemble in any Hilbert space dimension (finite or infinite), we prove that the error probability of the global pretty good measurement (PGM) is at most four times the sum of the optimal binary error probabilities. By constructing a family of regular-simplex ensembles, we further show that the coefficient four is optimal, even for arbitrary global measurements. This result improves on the pairwise bounds established by Cheng and Liu [arXiv:2606.06246 (2026)] and entails an explicit, sharp guarantee for the standard PGM itself. Our proof is also simpler: rather than constructing sequential measurements and applying a union bound, our proof relies on purely matrix-analytic techniques, combining a direct block Gram matrix analysis of the PGM error and a refined inequality between quantum Hellinger distance and Bures $χ^2$-divergence. Our analysis also yields a refined, one-shot pairwise Chernoff bound and explicit sufficient number of copies for a desired discrimination error.

Recursive state estimation often executes approximate numerical solutions inside a feedback loop, where highly accurate local steps do not guarantee better overall results. For a fixed linear Kalman model, we characterize when a correction within a prescribed subspace and norm budget can meet a local admissibility tolerance, and how the defects actually executed affect the finite-horizon covariance response. Centering each defect on the exact gain for the implemented covariance separates current solve error from inherited gain drift. Expanding the exact residual-drift identity reveals opposing quartic contributions beyond the quadratic response: innovation-covariance inflation enters positively, while local-gain reoptimization enters subtractively. Under matched initialization, an absolute sixth-order remainder bound, uniform over bounded defect sequences at fixed horizon, gives sufficient conditions for quadratic under- or overprediction. Machine learning proposes bounded corrections, while a learner-independent residual certificate and verified fallback govern execution of classical and quantum candidates without changing the reference estimator. In a power-grid tolerance study, learned correction lowers the minimum conjugate-gradient iteration count for deployment without fallback relative to uncorrected solves under the same residual certificate. Gains reconstructed from a variational quantum linear solver and from an annealing-based binary encoding, with small-scale terminal measurements on superconducting hardware and sampling on a quantum annealer, are executed through the same interface. By linking local repairability to nonlinear error propagation, the framework evaluates approximate solvers and learned corrections through independent certification and finite-horizon response, providing a practical basis for studying hybrid quantum--classical computation.

Score matching has driven major advances in classical generative learning by enabling models to learn from data without evaluating intractable normalization constants, or partition functions. Yet, extending this principle to quantum learning requires rethinking its foundations, as quantum states are described by noncommuting density operators rather than scalar probabilities. The noncommutativity creates fundamental challenges not only in defining quantum scores, but also in developing a training framework with efficient circuit implementations and rigorous theoretical guarantees. In this work, we bridge this gap by establishing a general quantum score-matching framework with end-to-end theoretical guarantees. Applied to Gibbs-state learning, our approach avoids additional thermal-state preparation and achieves information-theoretically optimal sample complexity in the high-temperature regime for Hamiltonians with bounded locality and interaction degree. This positions score matching as a new route to state-of-the-art performance in learning quantum Gibbs states. Beyond these theoretical results, numerical simulations show that our method remains effective even when gradients are estimated inaccurately under limited measurement budgets. Experiments on IBM quantum hardware further demonstrate that quantum score matching is NISQ-friendly: without any error mitigation or correction, it reduces the relative Hamiltonian-parameter error from 64% to approximately 10%. Together, these results extend score matching into an experimentally realizable paradigm for quantum-state learning.

This paper presents a hybrid quantum-classical framework for grayscale image compression and decompression, leveraging the strengths of quantum computing and deep learning. The compression pipeline integrates a Variational Quantum Daubechies Wavelet Transform (V-QDWT) and a trainable Quantum Convolutional Neural Network (QCNN) optimized end-to-end to achieve efficient, image-adaptive multi-resolution analysis and entanglement-based feature reduction. Input images are encoded using the Normal Arbitrary Superposition State (NASS) representation, enabling compact and scalable quantum storage. For decompression, we implement inverse QCNN and V-QDWT circuits to reconstruct coarse image features natively, followed by a classical Super-Resolution Generative Adversarial Network (SRGAN) to enhance perceptual quality. Experimental evaluations on benchmark grayscale datasets demonstrate the efficacy of our hybrid approach. By jointly training the quantum layers, the base quantum pipeline closely rivals classical JPEG2000 standards. Subsequent SRGAN refinement substantially pushes the boundaries of the reconstruction, achieving superior structural fidelity (PSNR: 30.0667 dB, SSIM: 0.8744, Histogram Correlation: 0.9244). Histogram analysis and qualitative comparisons further validate the restoration of fine textures and intensity distributions. Our findings highlight the potential of combining variational quantum compression with classical deep learning to enable efficient, scalable, and perceptually-aware image processing in quantum-enhanced computing environments.

Simulations of electrochemical materials and systems accelerate technological progress, but are still limited by computational power. In particular, quantum computing offers prospects for higher resolutions, due to the exponential amount of data that can be stored in a quantum state. As current quantum computers are still noisy, we consider a hybrid quantum-classical algorithm, that divides the problem into smaller computational tasks. We describe how to implement such an algorithm for non-linear partial differential equations, the Feynman-Kitaev Hamiltonian, in a scalable way for an electrochemical system. We show how it can evaluate general electrochemical models and present a quantum simulation of the Single Particle Model with electrolyte (SPMe) as the first quantum simulation of a battery cell.

Can entangled noise erase entanglement more efficiently than separable noise? Standard robustness restricts the added noise to separable states; generalized robustness allows any state. We prove that the two costs coincide for every two-qubit state and give an explicit full-rank qubit--qutrit state with a strict gap. Positivity under partial transpose (PPT) characterizes separability in both dimensions, so the boundary is not caused by a failure of the PPT criterion. Instead, product-vector geometry permits a rank-one bridge between the two-qubit dual optimizations and supplies a two-dimensional completely entangled subspace for the qubit--qutrit separation. Local isometric embeddings complete the finite-dimensional bipartite classification, also for any fixed multipartite cut. Combined with known three-qubit separation, the result classifies universal equality relative to full separability in all finite multipartite systems.

In this paper, we investigate the family of GHZ diagonal states, which are mixed multipartite quantum states that are diagonal in a GHZ type basis. We show that the class of GHZ diagonal states is highly symmetric and exhibits rich entanglement properties, making it relevant for applications in multipartite quantum key distribution.

Two types of non-Hermiticity found in physical systems, i.e., non-reciprocal couplings and complex potentials, have gained considerable interest recently. The former leads to the non-Hermitian skin effect, while the latter gives rise to a range of non-Hermitian symmetries such as parity-time ($PT$) and particle-hole symmetries. Although these two non-Hermitian forms have been incorporated in the same models, so far they have been treated as distinct families of non-Hermiticity. In this work, we establish an isospectral mapping between them using the Lanczos transformation. More specifically, we show that a generalized Hatano-Nelson model $H$ with non-reciprocal and spatially varying couplings can be mapped to a tight-binding model $H_L$ with real symmetric couplings and an imaginary on-site potential. This result holds even when the original $H$ already has an imaginary potential and exceptional points. Our work provides a refreshed understanding of the connection between different forms of non-Hermiticity. It also offers an approach to obtaining an intuitive physical understanding of exceptional points in $H_L$ that are elusive in $H$. Finally, our findings also warrant a versatile approach to constructing non-Hermitian systems with a complex potential and a real spectrum, without $PT$ symmetry.

Accurate simulations of non-Markovian quantum transport remain limited to small systems, and a key bottleneck is that each system site requires an independent set of quantum bath orbitals. We introduce the Stochastic Phase Algorithm (SPA), which replaces the independent local Gaussian baths in single-quasiparticle Holstein models by $R$ shared quantum baths with stochastic site-dependent phases. We prove that phase averaging reproduces the target two-point bath correlation matrix for every $R$, while increasing $R$ systematically suppresses errors from higher-order cross-site correlations. We obtain a fixed-time $O(R^{-1})$ trace-norm error bound with a prefactor independent of system size and connectivity. This spatial compression applies directly to unitary baths and can be combined with coupled-Lindblad spectral compression [Phys. Rev. Lett. 136, 090403 (2026)], which represents each shared environment by a very small number of coupled, damped quantum modes fitted to its thermal bath correlation over the simulation window. Numerically, SPA converges against direct unitary benchmarks on a $3\times3$ lattice, enables full-state-vector quantum-bath dynamics on a $100\times100$ lattice, and, with $R=1$, closely reproduces near exact benchmarks for exciton populations in bacteriochlorophyll aggregates and carrier mobility in rubrene.

The Dyson series expands the propagator of a time-dependent Hamiltonian in powers of the Hamiltonian, but its truncations are in general not unitary. The Fer expansion writes the same propagator as an infinite product of matrix exponentials, each of them unitary, and its remainder decays doubly exponentially with the number of factors. Convergence, however, is guaranteed only within a finite radius: the time integral of the norm of the Hamiltonian must be smaller than $2$. This is the best value known to date. Here we improve it by about $30\%$, raising it to about $2.6058$.

Cold atoms underpin quantum sensing, simulation and computation, but their coherent control demands highly stable optical fields whose generation, referencing and power scaling remain formidable integration challenges. While photonic integrated circuits have yielded compact visible lasers and high-$Q$ microresonators have enabled chip-scale optical frequency combs, these crucial technologies have largely remained functionally fragmented. Consequently, the coherent manipulation of ultracold quantum gases using a fully integrated laser-comb source has yet to be realized. Here we demonstrate a scalable, hybrid-integrated microcomb engine at 780 nm that seamlessly bridges frequency synthesis, atomic referencing and power amplification to achieve quantum state control of a Bose--Einstein condensate. By self-injection locking of electrically driven III--V lasers to high-$Q$ Si$_3$N$_4$ microresonators, we generate coherent platicon microcombs featuring 20- and 100-GHz mode spacings. Absolute referencing of the microcomb to an $^{85}$Rb transition actively suppresses long-term frequency drift from over 200 MHz to the 100-kHz level across 2,000 s. A selected comb tooth is subsequently injection-amplified to 102 mW, entirely preserving the microcomb's pristine coherence and stability. We utilize this synthesized field to construct an optical lattice, drive coherent two-photon Raman transitions, and prepare stationary spin-orbit-coupled and Raman-lattice states within an $^{87}$Rb condensate. By providing a synchronized optical grid, this atom-referenced microcomb allows multiple optical-control channels to scale without a proportional multiplication of independent frequency references. Our work establishes a transformative, fully integrated frequency-synthesis architecture essential for realizing deployable, large-scale atomic quantum systems.

Strong light-matter coupling offers a powerful framework for modifying molecular structure, dynamics, and optical response, yet achieving this regime at the single-molecule level remains a central challenge. Scanning Tunneling Microscope Break Junctions (STM-BJ) provide a promising route by combining single-molecule addressability with extreme nanoscale field confinement. However, the metallic environment that enables such confinement also introduces substantial plasmonic and excitonic losses, raising the question of how strong coupling can be realized in a metal-molecule-metal junction. Here, we identify the voltage as the key control parameter. We show that the applied bias not only drives the formation of an interfacial exciton through resonant charge transport but also suppresses its coupling to metallic loss channels. Simultaneously, the plasmonic cavity retains extreme mode confinement while the availability of modes is moderately tuned by voltage. Together, these results establish voltage-driven STM-BJs as electrically tunable single-molecule plasmonic cavities and open new routes for using the powerful STM-BJ toolbox, including quantum transport, tracking chemical dynamics, optoelectronics, and molecular-scale quantum control under strong light-matter coupling.

Broadband quantum memory devices are essential elements for future quantum networks. Here we propose a broadband quantum memory scheme called Hole Anti-hole Grating Echo Memory (HAGEM) for rare-earth ions in solids. We provide a Eu$^\text{3+}$ molecular complex with special hyperfine level structures of which the hyperfine level separations are in a specific mathematical correlation that can be obtained by harnessing chemical engineering. Using the memory protocol and material, we experimentally demonstrate a quantum optical storage efficiency of 14.9% and a memory bandwidth of 200MHz, which can easily be extended to a few GHz. With this demonstration, we show the first quantum application enabled by molecular engineering which cannot be achieved by any other existing Eu$^\text{3+}$ solid-state materials. In addition, we provide a framework for the chemical engineering of solid-state materials with rare-earth ions for quantum applications consisting of material design, synthesis & characterization techniques, and analytical methods for the quantum properties of rare-earth (RE) ions in solids. This work establishes a new direction in which molecular rare-earth ions can be used for a wide range of quantum applications, which cannot be realized by existing solid-state materials. This will greatly facilitate the development of molecular quantum emitter systems for real world applications.

Encrypted quantum cloning distributes an unknown $k$-qubit state among $m$ encrypted clones so that no individual clone reveals the input, yet the state can be recovered from any one clone together with a common quantum key. We ask the inverse question: for a fixed encoding architecture, which multipartite pure states can serve as exact resources for this task? For $m\ge2$, we completely characterize the pure resources compatible with a sector-wise two-Pauli encoder, with necessity holding for arbitrary completely positive trace-preserving (CPTP) recovery maps. For even $m$, exact recovery requires maximal entanglement across the signal--noise cut. For odd $m$, less entanglement can suffice, provided that the surviving signal correlations have the structure selected by the encoder. We further show, without fixing the encoder, that exact recovery from every authorized subsystem already implies perfect concealment of each individual signal and requires at least $(m-1)k$ ebits of signal--noise entanglement. For graph states, the resource classification reduces to an exact condition on the kernel of the signal--noise cut matrix, leading to binary certification and constructive Clifford recovery. We identify rank-deficient graph resources that attain the architecture-independent entanglement bound and prove that the entire Dicke family, including $W$ states, is excluded for every sector-wise two-Pauli encoder. Our results show that encrypted recovery depends not only on how much entanglement a resource contains, but also on how its correlations are organized relative to the encoder.

Although integrability does not universally require a continuous one-site symmetry, we rigorously prove that every jointly analytic, regular Yang-Baxter deformation of the qutrit exchange interaction necessarily retains a nontrivial, analytically varying one-site charge. Breaking this local symmetry imposes a fundamental physical constraint on approximate conservation, governed by the optimal uniform bound $δ^3 \le C\varepsilon$ that explicitly relates the minimal one-site symmetry defect $δ$ to the local current-conservation residual $\varepsilon$. While breaking all one-site charges strictly forbids an exact integrable completion, an optimally compensated nearest-neighbor interaction saturates this cubic limit and anomalously extends the guaranteed infinite-temperature energy-current correlation window to order $|λ|^{-3}$ in the perturbation strength $λ$. Furthermore, we reveal a fundamental resonance obstruction for intrinsic conversion perturbations that strictly prevents any exact first-order repair of a broken one-site charge on any finite ring. Nevertheless, we demonstrate that the complete eight-dimensional charge memory matrix remains thermodynamically protected and approaches the identity for timescales $t=o(|λ|^{-3/2})$, a robust feature of the full infinite-temperature dynamics when the thermodynamic limit is taken before weak coupling.

Fermionic Gaussian states are the workhorse reference states for qubit-based quantum simulation of fermionic systems, yet existing certification protocols either proceed via fidelity estimation, leading to suboptimal sample complexity in the target precision $ε$, only apply to Haar-typical states, or require adaptive measurements on a large fraction of qubits. We give an adaptive protocol that certifies any $d$-mode pure fermionic Gaussian state using $O(d^2ε^{-1})$ copies, single-qubit measurements with only one qubit measured adaptively per copy, and $O(d^3)$ classical processing time per copy. The $ε^{-1}$ dependence is optimal for the certification problem, even among strategies using entangled measurements. The sample complexity is controlled by the spectral gap of a $d\leftrightarrow d-2$ down-up walk---a Markov chain studied in the theory of high-dimensional expanders, equivalent to a two-site Glauber dynamics in statistical physics---relating certification efficiency to relaxation time to equilibrium. The worst-case bound is tight for this protocol and is attained by physically relevant states, including ground states of the fully dimerized Su-Schrieffer-Heeger (SSH) chain and BCS pair states. In contrast, numerics up to $d=14$ suggest that $O(d ε^{-1})$ copies suffice to certify Haar-typical Gaussian states, a factor of $d$ improvement over the worst-case bound. Finally, because the bound depends only on the target's computational-basis distribution, the protocol extends to efficiently phase-dressed states---states obtained by injecting an efficiently computable diagonal phase to Gaussian states---with the same sample complexity. The class includes a continuous family of four-mode non-Gaussian magic states for matchgate computation.

In quantum machine learning, training a quantum model requires each sample to be prepared as a quantum state by a loading circuit that must be re-executed for every shot at every training step. The total burden therefore scales with both the number of samples and the cost of preparation. Existing approaches reduce the loading cost of individual inputs or distill data and compress their representations before applying a separate quantum encoding. This separation can leave resulting samples costly to prepare or cause additional loss of the information during subsequent compilation into shallow circuits. We propose quantum dataset distillation (QDD), which distills the full dataset directly into a small set of shallow circuits. Each synthetic sample is parameterized as a staircase circuit corresponding to a low-rank tensor network, making the sample and its loading circuit the same object. The circuit parameters are optimized classically with exact gradients using distribution matching under an explicit loading budget, without post-hoc state-preparation synthesis. On MNIST and Fashion-MNIST, only 10 circuits per class ($0.0017\times$ the full dataset size) achieve accuracy comparable to full-data training and outperform selection baselines under matched sample and loading budgets. In finite-shot training, QDD reaches 95\% of the full-data accuracy with more than $100\times$ fewer cumulative shots. Additionally, we validate QDD on real quantum hardware, demonstrating its practical deployment potential.

Grover's algorithm is optimal in terms of oracle queries. We can trade accuracy for speed, which gives rise to the quantum partial-search algorithm. The partial-search algorithm is implemented using two kinds of Grover operators, global and local, where the former is the standard Grover operator for full search and the latter has a diffusion operator acting on the search subspace. The global-local-global sequence, also known as the Grover-Radhakrishnan-Korepin (GRK) algorithm, has been proved optimal in the oracle-query metric. In this work, we show that the alternating sequence of global and local Grover operators, formed by repeatedly applying a fixed product of global and local Grover operators, can achieve a lower expected circuit depth than the GRK algorithm. Through systematic analysis, we obtain its exact success probability, expected depth, and asymptotically optimal parameters. We derive the boundary, characterized by the ratio between the depths of the oracle and the global diffusion operator, separating the depth-optimal and oracle-optimal partial-search algorithms. When the depths of the oracle and the global diffusion operator are comparable, our proposed alternating partial-search sequence can reduce the minimum expected circuit depth by more than 20\% compared with the GRK algorithm.

A variety of quantum emitters compete in the quest for the best single-photon source for photonic quantum technologies. Consequently, only a consistent approach to analyze the second-order auto correlation function allows comparison of the multi-photon contribution ($g^{(2)}(0)$) of different sources. However, the community employs different and inconsistent methods for blinking sources, leading to incomparable benchmarks of source quality. Here, we use the emission of an inherently non-blinking quantum dot (QD) and apply artificial blinking through two different mechanisms: masking the recorded raw data in post-processing and emulation of a blinking system by gating the laser excitation pulses. We then compare the $g^{(2)}(0)$ values with the non-blinking result. For the analysis, we investigate five estimators of $g^{(2)}(0)$ actively used in the literature. While fitting the envelope of the correlations on long-time scales with the correct blinking model is the best choice, normalizing to the Poisson level gives by far the worst proximity. Furthermore, we test our predictive model to identify the underlying blinking mechanism of a QD in a circular Bragg grating cavity.

We propose a sub-Doppler cooling scheme for trapped-ion crystals in Paul traps. The combination of a hollow tweezer and microwave drive creates an effective two-level system which is cooled through attractive Sisyphus cooling. For ${}^{171}\rm{Yb}^+$ ions, we numerically identify optimal parameters for one- and two-ion crystals, and investigate the cooling rate in ion crystals with up to three ions. Our cooling scheme utilizes a single ion addressed with a tweezer to achieve sub-Doppler cooling of the $N$ axial motional modes perpendicular to the tweezer propagation direction, does not rely on the Lamb-Dicke regime and uses off-resonant light. We reach $1/e$ cooling times for the center of mass mode of $τ_{\rm com}<2$ ms, and a steady-state excitation number of $\bar{n}_{\rm{com}}\approx 0.7$. Our scheme is well-suited as an intermediate stage between Doppler cooling and ground-state sideband cooling, and can be readily realized in trapped-ion platforms.

In this paper, I address the problem regarding the physicality of Hilbert space in quantum mechanics, a topic brought into focus by Carcassi et al.'s paper "The unphysicality of Hilbert spaces" recently. I argue for the physicality of the Hilbert space in quantum mechanics, and demonstrate that there are inevitable ambiguity and arbitrariness if we want to identify the set of physical states with a proper subset of it. Moreover, I distinguish the ontological and modal reading of physicality from the pragmatic and operational reading of physicality, and then develop what I call the hierarchical view of physicality. According to this view, physicality is not a monolithic concept, but a layered one that admits degrees. I show the connection between the concept of physicality and modal metaphysics, and finally explain how it can be used to address the interpretational problem of quantum field theory brought by the existence of inequivalent representations.

We propose a framework for optimizing pulsed local oscillators (LO) for homodyne detection of multiphoton-number states by exploiting the tensor structure of their joint-spectral amplitude (JSA). We show that finding the optimal LO is equivalent to computing the JSA tensor's leading unitary eigenpair and that the factor matrices of the JSA's Tucker higher-order singular value decomposition (HOSVD) coincide with the Schmidt modes of the photon number state's single-particle reduced density matrix. We use the HOSVD to bound the optimal homodyne visibility and to initialize gradient based optimization. In simulated JSAs, weakly correlated, few-mode states reach near-unity visibility, with the leading HOSVD mode being the optimal LO, while strongly correlated, multimode states require full optimization and saturate below unit visibility even at the true optimum. These results offer a practical route to design LOs for homodyne detection experiments with realistic sources of photon-number states, which contributes to the practical implementation of sources of non-Gaussian quantum states.

We introduce a class of $2d$ quantum spin systems based on a unitary spherical fusion category with a chosen object. These models have frustration-free, reflection positive, but generally non-commuting local interactions, generalizing the Levin-Wen string-net models. Based on the theory developed in arXiv:2510.20662, we explicitly realize the Temperley-Lieb-Jones algebra, and more generally fusion spin chains as their boundary algebras.

Recent advances have revealed an interplay between quantum computing and topological data analysis (TDA). Most quantum TDA has focused on Betti numbers, which characterize the connectivity and ``holes'' of a dataset. Homology, however, contains additional information in the form of torsion: a nontrivial cycle can become trivial after being repeated finitely, revealing global constraints on how cycles combine and wrap around one another. Beyond applications in biomolecular studies, torsion appears in physical settings including homological quantum rotor codes, discrete charges, and gauge sectors. We study torsion from both classical and quantum perspectives. Given a graph $G$ and its clique complex $K = \mathrm{Cl}(G)$, we first prove that, for fixed $r$ and prime $p$, deciding whether $H_r(K,\mathbb{Z})$ contains $p$-torsion is NP-hard. As a corollary, when a homological rotor code is specified by $G$, deciding whether the code has a finite-dimensional logical sector of a given order is NP-hard. We discuss related problems, including the Bockstein homomorphism, Smith normal form, lattice saturation, and cohomology. Second, for a finite set of primes $P$, we develop a quantum algorithm that serves as a one-sided torsion witness. For fixed $r$, it outputs WITNESS or INCONCLUSIVE, i.e. WITNESS certifies that either $H_r(K,\mathbb{Z})$ or $H_{r-1}(K,\mathbb{Z})$ contains $p$-torsion for some $p\in P$ while INCONCLUSIVE makes no claim about its presence or absence. We identify a regime in which the algorithm achieves a near-quadratic quantum speedup over the corresponding classical algorithm under the same input model. Our NP-hardness result complements recent hardness results for estimating Betti numbers, adding a complexity-theoretic perspective to quantum TDA. Together, these results demonstrate that integral homology, beyond its Betti numbers, can be computationally challenging.

The Purcell effect has emerged as a powerful mechanism for controlling spontaneous emission and dissipation in cavity and nanophotonic systems; however, its realization in dissipative non-Hermitian hybrid platforms remains largely unexplored. In this work, we investigate the Purcell effect in a dissipatively coupled photon-magnon hybrid quantum system consisting of a yttrium iron garnet (YIG) thin film integrated with an inverted octa-ring resonator (IORR) in a planar geometry. To describe the underlying dissipative hybrid dynamics, we develop a quantum theoretical framework based on non-Hermitian coupled-mode theory combined with the input-output formalism. We also analyze the temporal decay dynamics of the photon-magnon system. Full-wave electromagnetic simulations demonstrate that the system can be engineered to operate in the level-attraction regime through dissipative photon-magnon coupling. By systematically tuning the magnon damping, we uncover the emergence of a Purcell regime in which cavity-photon dissipation is selectively enhanced through magnon-mediated loss channels. We further show that the saturation magnetization (Ms) provides an additional degree of control over the onset, tunability, and robustness of the Purcell enhancement. The combined modulation of magnon damping and Ms strongly influences the effective photon-magnon coupling, hybrid-mode evolution, and dissipation landscape, enabling precise control of hybrid quantum states. These findings establish a versatile strategy for engineering magnetization- and dissipation-controlled photon-magnon interactions in planar, chip-compatible architectures, opening new avenues for non-Hermitian cavity magnonics, tunable microwave dissipation engineering, and hybrid quantum information technologies.

Quantum sensing protocols usually presuppose where and when each signal acts, yet this information is unavailable beforehand in experiments such as scattering and radar. We show that causal agnosticity forces a measurement scheme to be interferometric even when only discrete interactions are allowed. Describing the sensing events in the recently developed quantum state over spacetime formalism, we then prove that the Fisher information of an interferometer is bounded by the squared sum of the local generator norms, independently of how the events are ordered. Nonunitary and spatiotemporally correlated signals can be explained as well when their physical dilation has a spacetime state on the enlarged events. Notably, the bound holds without presupposing a background spacetime that orders the events whenever the full collection of target and auxiliary events has a spacetime state. We show that this bound yields the spacetime Heisenberg limit and characterize its saturation through marginals of the spacetime state `dressed' by the signal. The $N^2$ scaling of the Fisher information with $N$ sensing events arises from the coherence of a single reference system shared across spacetime, whereas independently repeated interferometry obeys the standard quantum limit.

Prior work has explored quantum algorithms for topological data analysis (TDA), revealing the possibility of exponential quantum speedups in estimating the ratios of Betti numbers to the dimension of the combinatorial Laplacian. However, this quantity is only non-vanishing and efficient-to-quantumly-estimate when Betti numbers are exponentially large, a case for which concrete examples are rarely known. Furthermore, certain randomized classical algorithms are sometimes efficient in this regime. Thus, the prospect of achieving quantum advantage in conventional TDA appears fairly narrow. Here, we address these challenges to the quantum advantage in TDA by developing quantum algorithms for Mayer homology, which generalize simplicial homology to $N$-nilpotent boundary operators ($\partial^N =0$) and have recently been successfully applied to real-world TDA contexts. We introduce an efficient quantum algorithm for estimating Mayer Betti numbers and their persistent counterparts. We then prove that for high-order simplices, Mayer Betti numbers are often exponentially large in the dense regime, which ameliorates the normalization bottleneck of conventional quantum TDA. In the same regime, we argue that existing dequantization algorithms developed for conventional TDA, when applied to Mayer homology, generally lose theoretical guaranties, facing certain structural barriers that prevent their practical utilities. We also provide logical resource estimates revealing that a quantum computer with roughly a few hundred qubits and sixty million Toffoli gates could solve Mayer homology problems beyond the capabilities of known classical approaches. Finally, we discuss real-world applications of Mayer homology in genomics, supersymmetry, drug discovery, and neuroscience, revealing the potential of our quantum algorithm to deliver real-world impacts via Mayer homology.

A new wavefront sensing framework based on the interference of counter-accelerating Airy beams is presented. An engineered cubic phase function transforms a single Gaussian beam into two coherent Airy beams with opposite transverse accelerations, which self-recombine during free-space propagation to form an interference pattern encoding the aberrated incident wavefront. Numerical simulations demonstrate accurate recovery of the aberrated exit-pupil phase across the aberration sets considered, with a root-mean-square phase reconstruction error below $10^{-6} \mathrm{\;rad}$ for the aberration set shown and consistently low errors for the other sets, while maintaining accurate recovery in the presence of measurement noise. The approach eliminates collection optics and enables a compact wavefront-sensing architecture for applications where conventional interferometric systems are difficult to implement, including electron-optical systems, augmented and virtual reality systems.

For every fixed integers $r \ge 4$ and $2 \le k \le r-2$, we construct $r$-dimensional cubical sheaf complexes whose degree-$k$ CSS codes have positive constant rate, linear distance, and constant soundness, with bounded row and column weights. Taking $r=4$ and $k=2$ gives a family of asymptotically good binary qLTCs. At the core of our construction is a uniform product-expansion theorem for explicit Reed-Solomon codes on norm-one evaluation sets. The key point is that the expansion constant stays bounded away from zero as the local code lengths grow. We place these codes on arithmetic cubical complexes, obtaining constant local expansion for both the resulting sheaf and its dual. Together with the local-to-global framework of Dinur, Lin, and Vidick (FOCS 2024) and sheaf duality, this gives linear distance and constant soundness, while an asymmetric choice of local code dimensions gives positive rate. The resulting codes are explicit and polynomial-time computable.

We establish a sufficient condition under which overlapping PEPS boundary states satisfy the approximate factorization criterion for a spectral gap. The condition is formulated in terms of the boundary response induced by cutting bonds through the center of a rectangular region. We decompose this response into a contribution common to all four associated regions and a remainder measured in the instantaneous boundary metric. A single linear transport absorbs the common contribution and yields compatible factorization operators, with an error controlled solely by the remainder. We apply this framework to Ising PEPS and to the spin-3/2 AKLT model on the hexagonal lattice. For Ising PEPS, the required boundary-response estimate reduces to a Dobrushin-Shlosman-type condition. For the hexagonal AKLT model, a rooted expansion in paths and loops isolates the common response, while a local comparison of boundary states together with a scalar Kotecký-Preiss estimate controls the remaining terms. In both cases, the factorization error decays exponentially with the overlap width, up to a prefactor proportional to the cut length. For AKLT, we establish the corresponding physical projector estimate and obtain a uniform spectral gap. For Ising PEPS, the gap implication additionally requires compatible injective regional contractions, as specified in the paper. More generally, the method provides a systematic route from locality of PEPS boundary response to spectral gaps of two-dimensional parent Hamiltonians.

Which quantum measurement extracts the most classical information from an ensemble? We introduce the posterior algebra, a new canonical operator algebra selected by mutual information. For faithful ensembles, an affine information bound is exact precisely when this algebra is commutative; its joint spectral measurement is then optimal, and every optimal finite POVM refines it. Binary ensembles have one generator; compactness covers singular states, giving a proof of Shor's finite-dimensional binary orthogonal-measurement conjecture. The framework also gives rigidity bounds and a certified posterior-spectral receiver, validated on 408 mixed-state instances.

We introduce cavity Rydberg quantum photonics as a novel platform for generating hybrid entangled states of optical photons. The system achieves world-record sizes of these states and has the potential to produce yet larger states in the future. In the hybrid entangled state produced here, a superposition of two coherent states is entangled with a polarization qubit carried by a photon in another beam path. We perform quantum state tomography of this hybrid entangled state and evaluate various key properties. By optimizing the decoherence we increase the size compared to previous hybrid entangled states, reaching a size of $α^2= 2.4$. Besides the fundamental interest in Schrödinger cat states, this work is interesting because of potential applications in the field of quantum information processing.

Silicon-based spin qubits in Si/SiGe heterostructures are a leading platform for scalable quantum computing, yet bridging the gap between theoretical computer-aided design(CAD) models and experimental reality remains a significant challenge. Standard simulations often fail to capture critical physical phenomena, such as interface dipoles, parasitic charge accumulation, and the magnetic hysteresis of on-chip micromagnets. In this work, we present a comprehensive, experimentally calibrated 3D simulation pipeline for a 6-dot Si/SiGe device. We refine the semiconductor band alignment and introduce a semi-empirical classical charge screening model to accurately capture the formation of parasitic wells and their suppression of gate lever-arms. Furthermore, we apply the Jiles-Atherton model to account for the hysteresis and pre-magnetization of integrated cobalt micromagnets, successfully reproducing the experimental resonant frequencies across all six qubits. By coupling these calibrated electrostatic and magnetic profiles into a time-dependent rotating wave approximation (RWA) Hamiltonian, we reproduce experimental observables, including microwave power chevrons. This framework provides a robust foundation for predicting device behavior, evaluating microwave line losses, and optimizing future scalable spin qubit architectures prior to fabrication.

Finite-shot optimization can make noisy variational quantum eigensolver energies look artificially accurate. We studied six molecules on two IBM Heron r3 processors in eight replicated cells. Seven optimizer-selected values fell below the exact active-space eigenvalue by up to mHa. Independent later evaluation of the selected and final parameter points, differenced to remove a common epoch shift, showed that most of the selected advantage disappeared: the primary recovery was (approximate 95% session-level interval). Across the reported aggregation choices, recovery estimates ranged from 0.892 to 0.989. The measured contrast was consistent in scale with finite-shot selection, while calibration drift and other sources of variation remain possible. Accuracy claims based on best-observed hardware VQE values therefore require an independent check.

The fixed-angle conjecture for the quantum approximate optimisation algorithm (QAOA) is shown to be false for depth-2 QAOA on 9-regular graphs, and proven to be correct for depth-1 on any regular graph, as well, as for any depth on all 2-regular graphs.

We evaluate the Hellinger-distance coherence of the two-flavor neutrino state subject to Lindblad damping of the mass-eigenstate interference term, and obtain a closed expression in terms of the flavor-basis density-matrix elements. In the two-flavor vacuum treatment with negligible wave-packet separation, the undamped state is pure, and the smallest eigenvalue of the damped state grows linearly with $ε=1-κ$, where $κ=e^{-ΓL}$. An expansion about the pure state then yields a nonanalytic $\sqrtε$ correction to the Hellinger coherence, with coefficient $K=2\sqrt{2}\,u\sin2θ/\sqrt{1-2u}$, whereas the flavor-transition probability, the $l_1$ coherence, the concurrence, the entanglement of formation and the local quantum Fisher information all respond linearly in $ε$. Using representative Daya Bay, KamLAND and MINOS working points together with a current $90\%$ C.L. bound on energy-independent damping, we find fractional changes in the Hellinger coherence of $0.18\%$, $9.40\%$ and $21.51\%$, against $0.0009\%$, $0.43\%$ and $1.81\%$ for the concurrence. The comparison concerns the response of the quantifiers to the damping parameter and carries no implication about experimental resolution. The same mechanism operates, with a different coefficient, for a correlated dephasing channel acting on the flavor coherence, where the non-Markovian regime produces damped revivals.

We use quantum simulation to study how visible neutrino decay modifies the vacuum CP asymmetry in muon-to-electron oscillations within a $3+1$ neutrino scenario. The decay channel preserves CP symmetry, with CP violation arising from phases in the mixing matrix. We track the energy redistribution from visible decay and distinguish how parent attenuation and daughter regeneration modify the CP asymmetry. For the reference benchmark, the regenerated contribution is $4.85\times10^{-4}$, approximately $46\%$ of the total decay-induced shift. The full circuit for an effective two-energy model agrees with independent classical evolution. On an IBM quantum processor, we prepare the daughter state conditioned on decay and restore its physical normalization using fixed source and decay probabilities. After correction for measurement errors, the flavor-probability and coherence measurements both agree with the prediction within one standard error. Null controls test the suppression of the regenerated signal when daughter coherence or the relevant CP-sensitive mixing factor vanishes.

Quantum Rabi model (QRM) is a fundamental model in light-matter interactions (LMIs), whereas this finite-component system manifests infinite physics to be explored and a full understanding has not yet been reached after a hundred years since it was proposed. In the present work we create a geometric perspective for the QRM by mapping to a curved nanowire system, with curvature-induced spin-orbit coupling (SOC) manipulatable by LMI strength and frequency ratio, which is capable of revealing and perceiving the property universality and diversity from the ground state to the whole spectrum in a unified picture. Indeed, we unveil a super university in the adiabatic regime which manifests a universal scaling of spin texture ubiquitously valid for different couplings, different frequencies and different energy levels. The curve frame also facilitates our finding that a direction changeover of tangential spin swing emerges in the non-adiabatic spin texture in association with the quantum phase transition (QPT) in the QRM, which endows a geometric non-adiabaticity interpretation and connotation to the QPT. We also clarify that, among the curvature-induced effects, the SOC accounts for the spectral bifurcation and oscillations. Our method and analysis, readily generalized to other light-matter models, opens a dialogue between geometry and physics, thus paving a novel way to gain deeper insight into LMIs.

We present a unified study of charge and spin qubits encoded in a single interacting quantum dot tunnel-coupled to Rashba fermionic leads. The dot is described by an Anderson impurity Hamiltonian with either repulsive or attractive local interactions and a magnetic field of arbitrary orientation. In the repulsive regime, a spin qubit is encoded in the singly occupied spin sector, whereas in the attractive regime, close to the degeneracy between the empty and doubly occupied configurations, these two states define a charge-qubit subspace. We combine a weak-coupling Lindblad master equation in the Markovian secular limit with numerically controlled matrix-product-state simulations of the full dot-reservoir system. In equilibrium, we identify magnetic pair breaking in the attractive regime and a weak Rashba-induced magnetic anisotropy when the magnetic field is rotated relative to the spin-orbit axis. In the dynamical regime, relaxation and decoherence are controlled by the energetic gap between the logical manifold and nearby leakage states, and are further enhanced by Rashba-dependent tunneling. These findings show that even a minimal Anderson-impurity description captures key ingredients for coherent spin and charge qubits: the energetic structure of leakage states and spin-orbit-dependent dot-lead hybridization.

Gottesman-Kitaev-Preskill (GKP) states are widely studied as a bosonic encoding for fault-tolerant quantum computing because small displacement errors can be identified and corrected through syndrome measurements. However, fault-tolerant operation requires substantially greater GKP squeezing than is currently available in optical platforms. It is therefore important to identify quantum-information tasks that can be realised with finite-squeezing GKP states. Here, we study Bell nonlocality in finite-energy GKP Bell states under experimentally motivated measurement constraints. Although finite-energy GKP Bell states support Bell nonlocality even at low squeezing, logical Pauli measurements alone cannot reveal it. Accessing the maximum CHSH violation supported by the state generally requires logical non-Clifford rotations. We instead show that the required non-Gaussian resource can reside in the measurement itself. Photon-number-resolving detection combined with Gaussian preprocessing and adaptive feed-forward closely approaches the maximum violation of the CHSH Bell inequality without implementing logical non-Clifford gates. The same measurement principle strongly enhances Bell violations for cat-code Bell pairs and entangled coherent states, demonstrating that its usefulness extends beyond the GKP lattice. Our results identify non-Gaussian measurements as a practical route to revealing Bell nonlocality in finite-energy bosonic states.

Accurate measurement of an intended conditional phase does not by itself place a multiqubit phase gate in its declared generalized-gate equivalence class. We cast the diagnosis as structured Hamiltonian learning of the diagonal successful block in a known basis: Ramsey measurements on a connected graph reconstruct a target-relative eigenphase map; a Walsh transform then yields the per-cycle stroboscopic error generator in a selected logarithm branch, whose branch-dependent coefficients alone cannot decide global equivalence. For diagonal Pauli-Z dressing of weight at most m we derive an exact branch-independent criterion from multiplicative Boolean-Mobius invariants, converted at finite shot counts into a pass/fail/unresolved decision under prespecified tolerances and simultaneous confidence, separate from model rejection. For shared-control C^mZ gates a circular target-face contrast isolates each intended conditional phase, yet a support theorem exhibits forbidden interactions invisible to every target face once multiple targets or external spectators are present. We derive a Cramer-Rao bound for arbitrary integer phase contrasts, recovering the 4^m attempted-circuit scaling of a uniform (m+1)-body face, and quantify degradation from visibility loss, heralded survival, readout confusion, and correlated noise, while systematic bias triggers model rejection. Seeded simulations implement the 4M-setting multiplexed acquisition end to end: for M=3,4,5 at a common budget its mean phase-map RMSE is 0.689-0.794 times a separately compiled statewise scan, and a blind-interaction test yields 300/300 global-audit rejections versus 1/300 for target faces. These results estimate the error generator of a diagonal successful block under a specified acquisition model; they are not unknown-basis Hamiltonian identification, arbitrary-channel tomography, or hardware certification.

We propose a new method for measuring several characteristics of a fermion-boson medium formed during deep inelastic particle scattering. This method involves measuring the group and phase velocities of the accompanying wave process. The phase and group velocities of a wave process are related by the Rayleigh differential condition. The refractive index of a medium is determined by the phase velocity, while the group velocity characterises the medium's dispersion properties. In the case of deep inelastic $ep$ scattering under consideration, the wave process in an individual event is understood to be the exchange between an electron and a proton of an effective, non-perturbative mediator of interaction (${\cal B}$) with the quantum numbers of a neutral current. In the first report, we present new data on the group velocity of interaction carriers ${\cal B}$. We extracted the group velocity modulus values, $U_{_{\cal B}}^*$, from the HERA collider data using a formula derived from modified Heisenberg uncertainty relations and applying the indirect measurement method.. etc...(see preprint text)

Color centers in silicon carbide are a promising platform for quantum technologies, offering long-coherence electron and nuclear spins for storing and manipulating quantum information, as well as single-photon emission for quantum communication. Low photon collection efficiency is commonly addressed by integrating color centers into nanophotonic devices. Here, we report a scalable method for the deterministic integration of color centers into silicon carbide nanopillars, using the same nanoscale mask for both implantation of oxygen-related color centers (PL5, PL6) and subsequent nanopillar fabrication via dry etching. This approach solves the issue of low color center creation yield in nanostructures, with figures of merit comparable to bulk samples. We demonstrate count rate enhancements of up to one order of magnitude for PL5 and four times for PL6, while preserving spin coherence times. Our method is directly applicable to other solid-state platforms, offering a scalable route to efficiently integrate color centers into nanostructures.

Highly entangled and highly non-stabilizer quantum states need not be hard to learn. We give efficient algorithms for testing and recovering hidden tensor-product structure in unknown pure state vectors of the form $\lvertψ\rangle = U_C \bigotimes_i \lvertψ_i\rangle$, where $U_C$ is an arbitrary unknown Clifford unitary. Although the Clifford can thoroughly scramble the visible product structure, we prove that the Bell distribution retains a characteristic family of quadratic symmetries. By simultaneously block-diagonalising these symmetries, our algorithms linearize the problem and manage to recover both a disentangling Clifford and the hidden partitions with polynomial sample and computational complexity. This may be viewed as an extension of the abelian StateHSP paradigm in which classical post-processing exposes genuinely quadratic structure. Applied to Choi states, the method yields efficient proper learning algorithms for typical $t$-doped Clifford unitaries in regimes containing exponentially more $T$ gates than previously accessible: the required condition fails only for an exponentially small fraction of circuits when $t\sim n$, and continues to hold for a constant fraction even when $t=2n$. Our framework also provides tools for compressing structured many-body Hamiltonians and suggests benchmarking protocols for encoded logical product states in the early fault-tolerant regime.

Universal information extracted from a critical quantum state depends on how the state is probed. Spatial entanglement, participation statistics, and stabilizer Rényi entropy correspond to different replica geometries and need not isolate the same boundary data. We show that the complete distribution of Pauli magnitudes in critical Ising chains carries an exact geometric fingerprint of boundary termination, distinguishing lattice realizations that flow to the same infrared boundary fixed point. This structure is organized by discrete Selberg ensembles associated with the classical root systems $A$, $B$, $C$, and $D$: three open chains sharing the free--free Ising boundary condition retain distinct $B_L$, $C_L$, and $D_L$ trigonometric wall geometries. The standard symmetry-breaking representatives instead produce rectangular, pinned, and character-inserted $C$ ensembles. Their four boundary moments contain exactly two independent multiplicative combinations invariant under local endpoint normalizations. One of these reduces exactly at finite rank to a moment of the fundamental symplectic character and provides a lattice target for a defect--measurement-boundary junction amplitude. A conditional Gaussian-character law predicts its values throughout the unlocked phase, while exact-arithmetic finite-rank results at the $α=4$ transition depart sharply from the Gaussian continuation. These results show that the full Pauli spectrum resolves boundary information invisible to the infrared boundary fixed point alone and provide concrete targets for replicated boundary conformal field theory.

The fate of average symmetry-protected topological (ASPT) states based on the one-dimensional cluster state is investigated by using the Choi mapping, namely, the doubled Hilbert-space formalism. By introducing two effective spins, $τ$ and $η$, on each doubled rung, we obtain a transparent representation of the ASPT parent Hamiltonian and systematically identify the conserved stabilizers and the corresponding orders. We further study symmetry-preserving operations that deform the ASPT by combining qualitative effective-Hamiltonian and systematic parent-Hamiltonian analyses with numerical matrix-product-state filtering calculations. We find that although the ASPT remains robust over a broad range of decoherence strengths, strong-to-weak spontaneous symmetry breaking (SWSSB) becomes exact in the maximal-decoherence limit. In addition, we consider symmetry preserving no-click postselection, which removes the exact conservation law supporting the Rényi-2 string order of the ASPT and drives the system toward weak-symmetry spontaneous symmetry breaking (WSSB). Again, the ASPT remains robust over a broad range of postselection strengths, with WSSB becoming pronounced only near the projective limit and exact at the limit itself.

Local quantum interactions generate dynamics in an exponentially large Hilbert space, yet locality and entanglement restrict the information that can spread and accumulate. Bounds on propagation and entanglement growth, together with tensor networks, exploit these restrictions to discard information unnecessary for describing the evolution. This leads to a sharper question: how much information must any low-rank representation retain? Here we determine these limits, up to logarithmic factors, for short-range interactions. For time-independent evolution, the optimal rank obeys $\log D=\widetilde O(t+\sqrt{\log(1/ε)})$, with matching lower bounds fixing the accuracy exponent $1/2$; for arbitrary driving, matching fixed-time bounds instead give $2/3$. Correspondingly, the corresponding dynamical entanglement spectra exhibit distinct small-$α$ Rényi laws, $α^{-1}$ and $α^{-2}$. In one dimension, the static limit is constructively attained by an explicit MPO algorithm, with an analogous extension to Liouvillian dynamics. Together, these results determine the irreducible information required to represent local quantum evolution and uncover distinct entanglement structures in static and driven dynamics.

We present a distributed quantum algorithm that $3$-colors cycles in $O(1)$ rounds, with high probability. It follows that all locally checkable labeling problems (LCLs) that have round complexity $O(\log^* n)$ in the classical LOCAL model can be solved in $O(1)$ rounds in the quantum-LOCAL model, with high probability; this includes problems such as maximal independent set and maximal matching in bounded-degree graphs. This presents the first natural examples of graph problems with an asymptotic distributed quantum advantage for the LOCAL model; all prior examples that separate LOCAL and quantum-LOCAL are artificial problems constructed merely for the sake of demonstrating quantum advantage.

Distributed quantum computing requires fault-tolerant operations across inter-QPU links that can be substantially noisier than local gates. Uniformly increasing code distance provides additional protection but also enlarges data patches used for local storage and computation. Here, we introduce distributed heterogeneous-distance lattice surgery using an eight-data-patch ancilla-mediated (8-DAM) architecture, which will be useful for near-term quantum devices with less qubit overhead. In this architecture, the central ancilla spanning the inter-QPU boundary is enlarged while the data patches retain distance $d$. The protocol uses traveling stabilizers to suppress hook errors during merge and split operations between these unequal-distance patches. Circuit-level simulations of rotated surface codes at fixed local depolarizing noise show that logical-readout error rates depend only weakly on link noise. The resulting advantage over conventional lattice surgery grows as link errors increase. Comparisons with uniform distance implementations demonstrate comparable logical error suppression with reduced physical-qubit overhead. We also demonstrate how 8-DAM layouts support two simultaneous distributed logical CNOT operations between four logical data qubits using a single enlarged ancilla. At higher link noise, this construction yields lower logical error rates and more stability than two independent distributed logical CNOTs. These results support selective ancilla enlargement as a resource-efficient approach to fault-tolerant distributed quantum computing.

Spectroscopic frequency shifts due to residual motion of the probed atoms significantly contribute to the uncertainty budgets of state-of-the-art optical ion clocks. For clock transitions with second-order Doppler and quadratic Stark shifts of opposite signs, it is possible to configure electrodynamic ion confinement such that these two shift effects become anticorrelated causing zero net shift. Here, we introduce a spectroscopic interrogation protocol which leads, for systems with unknown and varying motional energy gain rates, to first-order auto-suppression of corresponding frequency shifts without requiring the opposite-sign configuration. We experimentally demonstrate the proposed method on a new ytterbium ion optical clock probing the 467 nm electric octupole (E3) transition, where the combined fractional uncertainty contribution from motion-induced frequency shifts is reduced from $1.3\times10^{-18}$ to $0.3\times10^{-18}$. An interleaved optical frequency ratio measurement against ytterbium's electric quadrupole transition (E2) at 435 nm delivers an E3/E2 frequency ratio of $0.932 \,829 \,404 \,530 \,965 \, 340 (39)$. Combined with previously published ratio data this leads to a limit for a potential fractional temporal variation of the fine-structure constant of $2.4 (2.7) \times 10^{-19}/$yr, in agreement with existing bounds.

Decoherence free subspaces are a steady-state structure of the open quantum system which preserves quantum coherence between the states lying with in it and thus has found a variety of applications throughout quantum information science and technology. In this paper we study the computational complexity of deciding whether an open quantum system admits a decoherence free subspace or not. More specifically we study this problem with in the context of Markovian open quantum systems, governed by the time-independent Lindblad master equation. Along the way we introduce the $k$-Local Lindbladian problem, which captures the difficulty of computing purity decay rates under Lindbladian dynamics. We show that both problems are hard for the complexity class Quantum Merlin Arthur (QMA) when the locality $k \geq 5$, with the first under perfect completeness and the second being complete for QMA. Our hardness construction generalizes Kitaev's clock Hamiltonian construction to the open quantum system setting by encoding the execution of a quantum circuit into the steady subspace of a Lindbladian containing both pure and mixed history states. This subspace is then mixed depending on the output of the encoded circuit. Our results suggest that deciding whether a generic Markovian open quantum system admits a decoherence free subspace is intractable even for quantum computation.

We study the transmission of two independent confidential classical messages over a quantum broadcast channel, one for each receiver. Each message must remain secret from the other receiver, including when that receiver knows its own message. For classical inputs and quantum outputs, we establish the classical Marton-type inner bound under average reliability and conditional strong secrecy. The encoder selects pairs of codewords from independently generated codebooks using normalized likelihood weights. We prove reliability through a change-of-distribution argument. Our main technical result is a bipartite classical-quantum resolvability theorem that accounts for the dependence created by pair selection and establishes secrecy for the same encoder. We also obtain a multi-letter capacity characterization and extend it to arbitrary quantum inputs under secrecy against the other receiver, together with the Stinespring environment. We recover confidential capacity regions for deterministic classical and degraded classical-quantum channels, with an explicit evaluation for the classical Blackwell channel. For coherent isometric extensions of injective deterministic classical broadcast channels, we show that the confidential classical capacity region equals that of the corresponding classical channel. We then compare confidential classical communication with quantum transmission. For the coherent isometric extension of the Blackwell channel, we determine the unassisted quantum-capacity region and show that some achievable confidential classical rate pairs lie outside it. The Platypus channel provides another example of this separation.

We construct an explicit family of finite-dimensional quantum channels for which the optimal classical communication rate achievable with product-state codewords and collective decoding tends to zero, while rates achievable using entanglement only within pairs of channel inputs grow without bound. Our construction combines deterministic qudit Clifford unitaries with a binary measurement and classical feedforward, providing a derandomization to Hastings' probabilistic construction. The key ingredient is a careful design of measurement and feedforward process that yields the required one-copy and two-copy output entropy bounds from moment estimates alone, without requiring strong convergence of the underlying unitary family.

Modular quantum computing is a leading candidate for scalable fault tolerant quantum computation. Performing lattice surgery using surface code patches in different modules requires the use of inter-module gates that are noisier than the local gates. Furthermore, the merged layouts during lattice surgery expose multiple directions in which hook errors can propagate to reduce the fault distance. Existing hook-avoiding schedules either increase the syndrome extraction circuit depth, or let link faults propagate into the bulk. We introduce a seam construction that allows splitting arbitrary merged rotated surface code layout into smaller patches with uniform boundaries that could keep their own hook-avoiding N/Z shaped schedule. At the seam we split weight-4 stabilizers into pairs of weight-2 stabilizers that are mediated through a Bell pair and measured within a CNOT depth of 4. We also employ the use of three-qubit $\texttt{CXX}$ gates for parity measurements at the seam to maintain the minimum CNOT depth. Through this seam construction, we confine the elevated link error at the seam, protecting the bulk from higher error rate. We also give a custom detector annotator for such seams that can find the detector space, annotate detectors in the Stim circuits, and ensure that they are suitable to use by matching decoders. We implement our construction for the logical Pauli-$XX$ measurement lattice surgery and a cross-shaped spatial junction and sweep the link error rate from $10$ times to $100$ times a fixed bulk error rate, and show that our construction gives the lowest and most stable logical error rate than the other frameworks compared here.

We construct quantum locally testable codes (LTCs) with constant rate, distance, soundness and locality under a variant of a product expansion conjecture of Bafna and Vyas about Reed-Solomon codes. In particular, we use the high-dimensional expansion framework of Dinur, Lin and Vidick for constructing quantum LTCs, instantiated with the non-Abelian cubical complexes of Rungtanapirom, Stix and Vdovina. Our code is obtained by equipping the complex with carefully chosen Reed-Solomon local codes whose symmetries are compatible with those of the complex.

We investigate the microwave response of sputtered Nb films as a function of biaxial film stress. Although transport measurements show nearly identical superconducting transition temperatures ($9.0\pm 0.2$K) and residual resistance ratios across the stress series, microwave resonators fabricated from highly compressive films exhibit enhanced temperature-dependent loss and larger frequency shifts. A conventional single-phase Mattis--Bardeen description yields an effective critical temperature of $2.4\pm0.2$K, approximately a factor of four below the value obtained from transport measurements. We show that the data are instead consistent with the presence of an additional low-gap component whose contribution increases with compressive stress. These results show that conventional transport measurements can overlook stress-dependent low-energy excitations that strongly influence microwave performance.

In the welded tree problem, an algorithm is tasked with navigating a graph formed from two binary trees joined at the leaves through a ``weld'' of connecting edges. A quantum walk can navigate from root to root exponentially faster than any classical algorithm. However, known efficient quantum algorithms cannot find a path between the roots, as recording the path destroys constructive interference and thus the speedup. We prove that this is inherent: any quantum algorithm needs exponentially many queries to find a path between the roots of an independently matched welded tree graph. This provides an example of a problem that a quantum computer can solve exponentially faster than any classical algorithm by exploring exponentially many paths in superposition, but where it is provably intractable to find any such path. The proof uses compressed permutation oracles to record the progress of a quantum algorithm as it queries the graph. We show that the compressed database remains path-free up to a small error. By controlling such errors and bounding the progress of the algorithm with each compressed oracle query, we show that $Ω(2^{n/12})$ queries are required to find a path in a height-$n$ tree with constant success probability.

A fundamental question in physics is: When does classical behavior emerge from quantum systems? Bosonic Gaussian states provide a natural setting to explore this quantum-classical boundary, as they capture both the classical field behavior and the intrinsic quantum nature of light. Here, we address this problem from a learning-theoretic perspective by asking: When are bosonic Gaussian states classical to learn? That is, under what conditions (if any) can an n-mode bosonic Gaussian state be learned with as few samples, and with operations as simple, as are needed to learn a classical 2n-variate Gaussian distribution? We establish a smooth crossover in learnability governed by the state's thermal fluctuations: - Cold Gaussian states are non-classical to learn: When the covariance matrix satisfies $Σ\le(\frac12+O(\frac1n))I$, i.e. close to the vacuum covariance, tomography under single-copy (i.e., non-entangled) measurements fundamentally requires $Ω(n^3)$ copies, strictly exceeding the sample complexity $Θ(n^2)$ of learning classical Gaussian distributions. We show that this hardness persists even when few-copy entangled measurements are allowed. - Warm Gaussian states are classical to learn: When thermal fluctuations exceed the vacuum noise, parameterized by $Σ\ge(\frac12+ν)I$ for any parameter $ν>0$, we prove that single-copy tomography requires $N=Θ\left(n^2\min(n,1+ν^{-1})\right)$ copies. This bound is tight and is achieved by simple, non-adaptive, unentangled heterodyne measurements. Crucially, for $ν=Ω(1)$, the sample complexity drops to $Θ(n^2)$, matching the classical case. Our results tightly characterize a quantum-to-classical crossover in the learnability of bosonic Gaussian states, reveal a novel connection between fundamental physics and statistical learning theory, and have implications for real-world sensing experiments.

We achieve nontrivial transversal logical multi-controlled-$Z$ gates with asymptotically optimal parameters simultaneously on quantum low-density parity check codes and quantum locally testable codes, by applying the gate framework of [arXiv:2604.01874] to the recent good qLTC construction of [arXiv:2609.20780]. To this end, we use the covering space method to construct a nonzero cup product pairing on a finite arithmetic cubical complex. This differs from the previous construction of almost-good codes, whose base space is a hypergraph product. We express the pairing as a coefficient in a product of Moore determinants and prove polynomial nonvanishing by a bipartite multigraph specialization. We then construct covering spaces to obtain an asymptotic family of good qLTCs on which the pulled-back pairing induces the desired nontrivial transversal logical action.

Quantum strong direct-product theorems for specific functions have been known for nearly two decades. These have been extended to general results for function computation and state generation. The proofs of these results use a version of the multiplicative adversary method that does not naturally extend to relations. Standard strong direct-product theorems apply when algorithms must correctly answer every given question. Prior work extended them to equivalent threshold direct-product theorems, which require answers to all questions but only require that most answers are correct. We focus on two further generalizations. Strong selective direct-products apply to algorithms that adaptively choose, based on what they learn from queries, which questions from a large list to answer. This generalization is relational and useful for proving time-space tradeoffs. We prove a quantum strong selective direct-product theorem for all functions using a new multiplicative adversary formulation for relations that satisfies a strong selective direct product property while being strong enough to capture any query lower bound for functions proven by negative-weights adversaries. This was not previously known even without selectivity. The second generalization is list-decoding direct product problems introduced by Ben-David and Blais for classical randomized query complexity. These allow an algorithm to produce a large list of possible output vectors such that one of them is fully correct. They proved that such theorems hold for classical randomized complexity of all Boolean functions. We prove a quantum analogue of this theorem for all partial Boolean functions. We show that strong list-decoding direct-product theorems are implied by a special case of multiplicative adversaries which we show, via a new reduction, can be obtained from negative-weights adversaries for any Boolean-valued function.

Understanding the resources required to generate approximately random unitaries over various groups is a natural goal of quantum information theory. With respect to one notion of approximation, that of a design, it is known that the full unitary group can be approximated in logarithmic depth by one-dimensional circuits of nearest-neighbour 2-local gates. On the other hand, remarkably, circuits with this connectivity cannot form designs over the matchgate group in sublinear depth. Here we show that this dramatic slowdown can disappear when using a general qubit connectivity graph $\mathsf{G}$ of routing number ${\rm rt}(\mathsf{G})$. Indeed, in this setting one can obtain (strong) $\varepsilon$-approximate relative error matchgate $k$-designs in depth $\mathcal{O}(k^2{\rm rt}(\mathsf{G})\log n\log(n/\varepsilon))$. For all-to-all connectivity, ${\rm rt}(\mathsf{G})=2$. Our construction is conceptually simple, involving a random walk on the matchgate group, and no ancillae. As a technical byproduct, we improve upon the state of the art for fermionic routing, obtaining an $\mathcal{O}({\rm rt}(\mathsf{G})\log n)$ depth router. Additionally, for $k=3$, we obtain an exact strong matchgate design in $\mathcal{O}({\rm rt}(\mathsf{G})\log n)$ depth, again without ancillae. Under all-to-all connectivity, our fermionic router and 3-designs are optimal. Notably, our results imply that quantum algorithms for fermionic tomography which require drawing from a matchgate 3-design may be exponentially sped up on quantum computers with all-to-all connectivity, relative to their strictly one-dimensional counterparts.

Photon statistics have moved to the forefront of modern optics, as intensity fluctuations and correlations shape multiphoton interactions and reveal information beyond mean-intensity measurements. Developing high-quality photon sources with pronounced correlations is a fundamental necessity in these fields. Here we demonstrate fluctuation-driven nonlinear statistical amplification of quantum light in spontaneous four-wave mixing using filtered amplified spontaneous emission (ASE). Extending the coherent-pump framework to fluctuating fields, we show how nonlinear weighting of pump intensity combines with bosonic bunching to amplify quantum statistics and reshape temporal correlations. In a SiN microring, ASE pumping increases the zero-delay unconditional second-order correlation from 2.01 to 7.58 and extends the Hanbury Brown--Twiss correlation time by a factor of approximately 2.4. The super-bunched quantum source nevertheless retains heralded single-photon behaviour with $g_H^{(2)}(0)\simeq0.04$, while the same ASE pump supports time--energy entanglement in a silicon waveguide with a raw Franson visibility of 89.84\%. These results establish driving-field statistics as a design dimension for quantum light, broadening the horizons for research into higher-order correlations and nonlinear physics.

Bosonic codes offer a promising approach towards hardware-efficient fault tolerance, with many leading examples such as the cat-code and the GKP code organized by an underlying symmetry. We build on a representation-theoretic framework of quantum error correction to formalize the construction and analysis of multimode symmetric bosonic codes, focusing on finite groups. Here, a physical, logical representation and an initial seed state together define the codewords via a covariant encoding. A central observation is that QEC matrices can be viewed as morphisms of group representations, so that Schur's lemma forces entire irreducible representations blocks to vanish. We recover several known single- and two-mode bosonic codes and build and analyze the error protection capabilities of three codes based on finite subgroups of SU(2). We analyze the impact of reducibility of the logical representation and optimize the seed state using the near-optimal fidelity.

The choice of probe state is essential to achieving ultimate precision in quantum metrology. For a single parameter, an equal superposition of eigenstates associated with the largest and smallest generator eigenvalues is optimal. This simple construction does not directly extend to multiple parameters, since different parameters can favor different probes. We address this difficulty through a geometric construction of optimal probes for multiparameter estimation in distributed quantum sensing. In this setting, the generators commute and share a common eigenbasis, so each common eigenstate defines a vector of generator eigenvalues. We show that the minimal enclosing balls and ellipsoids of these vectors determine the maximal total quantum Fisher information and the minimum weighted covariance, respectively. In both cases, the boundary of the convex body identifies the common eigenstates that can contribute to an optimal probe, and its center and shape specify the conditions that their populations must satisfy. Our results provide a systematic approach to designing optimal probe states, linking the structure of the parameter generators directly to the attainable precision in multiparameter quantum metrology.

We study Hamiltonian learning for $k$-local Hamiltonians at large step size, using only forward time evolution at integer multiples of a fixed time interval. For this task, our new technique, which we call eigenphase engineering, achieves Heisenberg-limited learning with a step size that is optimal up to logarithmic factors. For an unknown $s$-sparse Hamiltonian with fixed locality $k$ and $\|H\|_{\mathrm{op}}\leqΛ$, our algorithm recovers its Pauli coefficients to $\ell_2$ error $\varepsilon$ in total evolution time $\widetilde{O}(s/\varepsilon)$, matching the best known scaling while allowing a near-maximal step size $\widetildeΘ(1/Λ)$. As an independent contribution, we strengthen the evolution-time lower bound to $Ω_k(s^{1-1/(2k)}/\varepsilon)$, placing our algorithm within a factor $\widetilde{O}(s^{1/(2k)})$ of being optimal. Eigenphase engineering departs from approaches based on dynamical approximation or iteratively canceling the unknown Hamiltonian. It encodes energy expectation differences in the perturbative response of eigenphases of the actual controlled evolution, then extracts them through phase estimation and high-order extrapolation. This avoids the need for polynomially shorter evolution steps as the target precision improves. A version using only single-qubit operations retains the same step size with a $\sqrt n$ overhead in $\ell_2$ learning time for $n$ qubits. The method also enables tolerant Hamiltonian certification and estimation of a specified Pauli coefficient, the latter without locality or sparsity assumptions. These results establish eigenphase engineering as a versatile approach to extracting Hamiltonian information with infrequent control.

We use a new technique for manipulating controlled quantum circuits to convert between two distinct types of quantum adders, one based on the Quantum Fourier Transform and the other based on the Ripple-Carry technique from classical reversible logic. This conversion takes the form of an explicit gate-level transpilation. We also present a new quantum adder with a natural interpretation as a kind of Carry-Lookahead adder that uses no ancillas.

Optical-rotation measurements benefit from increasing probe photon number, but their performance is often limited by detector saturation and technical noise in the optical readout. Here we introduce preselection-encoded weak-value amplification (PeWVA), in which the quantity of interest is encoded into the probe polarization before a downstream weak-value interferometer. This architecture separates the sensing interaction from the postselected readout, enabling tunable local amplification while reducing the optical power delivered to the detector. We show that PeWVA does not create additional Fisher information, but offers a practical advantage when detector dynamic range is limiting. We further analyze coherent stray light and phase fluctuations and show reduced conversion of these perturbations into equivalent rotation errors. Using an $^{87}$Rb $M_x$ atomic magnetometer, we experimentally demonstrate substantially improved magnetic-field readout under detector-constrained conditions using both transimpedance-amplified and avalanche photodiodes. The experiments also confirm reduced susceptibility to vapor-cell-induced stray light and interferometer phase modulation. These results establish PeWVA as a detector-constrained optical readout strategy with enhanced tolerance to representative interferometric perturbations.

Ergotropic-gap relations provide thermodynamic witnesses of quantum correlations, but a direct dynamical connection between extractable work and entanglement remains largely unexplored in multipartite non-Gaussian bosonic systems. Here, we establish such a connection for a bosonic quantum battery driven by a coherent-state superposition. Despite the infinite-dimensional Hilbert space, the dynamics retains a simple structure that allows the relevant work and correlation measures to be obtained exactly. We show that the loss of extractable work associated with the passive part of the battery energy is directly determined by charger-battery entanglement. This relation also separates the charging power into contributions from energy transfer and from changes in the battery spectrum. At the same time, multipartite correlations are progressively redistributed from charger-involving correlations to correlations internal to the battery. For a symmetric resonant protocol, complete energy transfer coincides with charger-battery disentanglement and fully extractable stored energy, while multipartite correlations within the battery are maximal. Individual cells, however, remain mixed, revealing a distinction between global and local work extraction. We further show that, in the regime considered, locally extractable work is entirely supported by energetic coherence. Under single-photon loss, the analytical structure survives, but environmental correlations separate charger disentanglement from maximal work extraction.

Probability backflow is investigated for charged spin-$1/2$ particles in a uniform magnetic field within the lowest-Landau-level approximation. While single-mode Landau states exhibit only weak and non-robust backflow, it is shown that two-mode interference gives rise to negative probability flux in both the Schrödinger and Pauli formulations. In the Pauli case, orbital and spin contributions to the probability current are explicitly separated, revealing an additional interference mechanism. The external magnetic field is found to act as a tunable control parameter, simultaneously controlling the spatial overlap of orbitals and the spin dynamics. In the two-mode regime, a resonance between orbital mismatch and spin precession leads to an enhancement of backflow. Finite spatial resolution is shown not to suppress the effect within realistic coarse-graining. These results establish magnetic-field-controlled quantum backflow in Landau systems as an accessible interference phenomenon.

Simulating strongly correlated fermions remains a long-standing challenge due to the exponential complexity of the Hilbert space and the intricate sign structure of many-body wavefunctions. We introduce a variational framework centered on a neural network backflow transformation that combines deep learning with variational Monte Carlo. The proposed ansatz employs a multi-determinant expansion with low-rank shifts to capture non-local correlations and complex sign structures. Applied to the two-dimensional Hubbard model at both half-filling and $1/8$ doping, the method achieves energies within $0.45\%$ of auxiliary-field quantum Monte Carlo at half-filling and captures intertwined charge- and spin-density stripe patterns at $1/8$ doping. These results demonstrate the potential of this framework as a scalable and interpretable approach to variational simulations of strongly correlated fermionic systems.

Dynamic circuits, which incorporate mid-circuit measurements and classically controlled operations, extend the expressive power of quantum programs and are central to applications such as quantum error correction, state preparation, and distributed quantum algorithms. However, their classical simulation is challenging due to the exponential growth of execution branches induced by mid-circuit measurements. In this work, we develop a tensor network approach for simulating dynamic circuits by extending a DMRG-based method for quantum circuit simulation to support dynamic circuit operations. To address the exponential proliferation of execution branches, we introduce and compare two strategies: a single-path stochastic approach that samples individual measurement outcomes, and a multi-path approach that maintains an ensemble of branches. We benchmark these methods on standard dynamic circuits, including the teleportation protocol and GHZ state preparation, as well as on random dynamic circuits. Our analysis explores the trade-offs between simulation accuracy and computational efficiency. These results provide a practical and scalable framework for the classical simulation of dynamic circuits.

Driven-dissipative many-body quantum systems can be exploited in quantum enhanced sensing protocols. Here, non-classical correlations may allow one to reach a measurement precision that surpasses the standard quantum limit. The relevant figure of merit for assessing such quantum advantage is the quantum Fisher information (QFI). In a many-body setting its computation is challenging as it requires knowledge of the full system-environment state. Here we make use of a field-theoretical approach, which is particularly well suited for systems with many degrees of freedom. In particular, we show that the QFI can be linked to a Keldysh path-integral. This route leads to a semiclassical expression of the QFI, which is obtained through a controlled expansion in the so- called quantum fields. We benchmark the framework on three systems of increasing complexity: the driven-dissipative harmonic oscillator, the boundary time crystal - which becomes semiclassical at large system sizes - and a two-dimensional array of collectively emitting atoms. We assess in which parameter regimes the semiclassical description holds and gives access to system sizes beyond the reach of exact methods.

Strong-to-weak spontaneous symmetry breaking (SWSSB) can occur in a maximally mixed charge sector even when ordinary charged correlations vanish. We study this order when a charge sector splits into dynamically disconnected fragments. In a one-dimensional $t$-$J_z$ chain with species-resolved dephasing, each fragment is labeled by a conserved spin word. A charged transfer between separated finite intervals preserves that word only if the intervening spins satisfy a periodicity constraint. In the full-state two-point sense, we use this constraint to prove the absence of long-range fidelity and Rényi-1 order in typical fixed-composition fragments, uniformly over all norm-bounded charged operators in any prescribed finite interval. A fragment with primitive spin-word period $k$ supports a $k$-particle channel with exact long-distance value $ν^k(1-ν)^k/k^2$, and no charged operator on fewer than $k$ sites can carry this order. A transverse exchange connects the fragments while preserving the global charges and restores the full-sector steady state at finite size. The conserved spin word therefore selects the local channels that can support mixed-state order.

Secure multiparty computation (MPC) enables mutually distrustful parties to compute on private digital inputs. We initiate the study of spatiotemporal MPC, extending this paradigm to functionalities whose inputs additionally depend on physical facts such as the parties' locations, times, or trajectories. Such protocols must simultaneously hide spatiotemporal information and ensure its physical consistency: a malicious party should not be able to make the functionality operate on a spatiotemporal input inconsistent with its actual physical state. The main conceptual challenge is to formulate extraction of spatiotemporal information within the simulation-based security framework. We introduce arguments of spatiotemporal knowledge, following the principle "I prove, therefore I am:" rather than defining physical presence directly through a mathematical relation, we define it operationally through the ability to complete a sound spatiotemporal verification protocol. Accordingly, an extractor recovers a spatiotemporal point from a successful prover and certifies its physical validity by using the extracted prover to succeed in an auxiliary spatiotemporal verification protocol. Building on this notion, we define universally composable (UC) security for spatiotemporal MPC, capturing privacy, physical consistency, and composability. We provide constructions achieving this new MPC notion. We first construct UC-secure commit-and-prove of spatiotemporal knowledge: in the CRS model under LWE against quantum provers without pre-shared entanglement, and in the QROM against quantum provers with unbounded pre-shared entanglement. Using these protocols, we obtain UC-secure spatiotemporal MPC from semi-honest post-quantum MPC. We also extend our framework to support quantum functionalities with classical spatiotemporal input.

In this paper we analyze the performance of photonic CZ gates based on N waveguide-coupled cavities containing two-level emitters. We derive single- and two-photon scattering matrices for one cavity using the input-output formalism of quantum optics and for N>1 cavities using the SLH formalism, allowing us to compute the CZ gate fidelity. We consider two input Gaussian wave packets that are centered on a two-photon transition of the emitter-cavity system, and find a trade-off between optimizing the single-photon and two-photon wave packet shape. While the single-photon wave packet is preserved for large emitter-cavity coupling rates, where there is little overlap with the single-photon transitions, the two-photon wave packet acquires the necessary $π$ phase shift for smaller coupling rates, comparable to the cavity decay rate multiplied by the number of cavities. We find that this trade-off limits the CZ gate fidelity to approximately 60% when averaging over all input states.

Simulating the dynamics of dissipative quantum many-body systems governed by local Lindbladians is a fundamental task in quantum computation. While the near-optimal gate count has been achieved for Hamiltonian simulation, comparable results for Lindbladian simulation remain elusive. In this work, we develop quantum algorithms for lattice Lindbladians by exploiting their locality. First, we consider sparsely dissipative systems, in which the dissipation is sparsely located, including boundary-driven systems. We establish a near-optimal quantum algorithm for their dynamics with gate count $O(Nt \, \mathrm{polylog}(Nt/\varepsilon))$, where $N$ is the system size, $t$ is the evolution time, and $\varepsilon$ is the allowable error. We then consider generic lattice Lindbladians with finite-range interactions and dissipation, and develop an algorithm for simulating time-evolved observables with gate count $O((Nt)^{4/3} \, \mathrm{polylog}(Nt/\varepsilon))$ per sample with the sampling complexity $Θ(\varepsilon^{-2})$. The gate count has the smallest known dependence on the system size among algorithms retaining polylogarithmic dependence on $1/\varepsilon$. Our algorithms are based on two techniques that exploit locality: patching and merging. Patching decomposes dissipative dynamics into dynamics on subsystems with exponentially small error, generalizing a key idea underlying the Haah-Hastings-Kothari-Low algorithm for near-optimal Hamiltonian simulation. Merging absorbs reversed dissipative dynamics into other parts of the evolution, substantially reducing the overhead associated with quasi-probabilistic sampling. These results demonstrate that locality can be fully exploited to achieve fast quantum simulation of dissipative many-body dynamics, opening the way to applications such as predicting nonequilibrium phenomena and preparing desirable quantum states.

The realization of entanglement distribution (ED) in large-scale quantum networks (QNs), as a fundamental theoretical framework of quantum communication, faces significant challenges. Percolation theory, drawn from statistical physics, has been identified as a potential solution to this problem. Nevertheless, when addressing ED, percolation theory primarily relies on numerical simulations and approximate algorithms. This approach often lacks interpretability and controllability for many phenomena occurring during the ED process in large-scale networks, including emergent phenomena near the threshold. To address these limitations, in this paper, we {focus on} leveraging operator theory to construct a mathematical framework for entanglement percolation in series-parallel QNs. Through the application of operator-theoretic methodologies, we analyze several critical issues within the entanglement percolation process.

Entanglement embezzlement asks how much entanglement can be borrowed from a many-body state by local operations and classical communication while returning that state with a small error. We uncover a conservation-law mechanism that redistributes the dominant probability mass of the Schmidt spectrum in the logarithmic Schmidt-rank coordinate and thereby controls this operational resource. For typical random pure states at fixed U(1) charge, we prove a finite-error conversion law: away from half filling, the charge bias converts $O(\sqrt L)$ charge fluctuations into $O(\sqrt L)$ borrowable entanglement, whereas particle--hole symmetry at half filling removes this contribution entirely. We then show how the resource develops dynamically in charge-conserving random circuits. Combining hydrodynamic analysis with large-scale replica tensor-network calculations, we find that diffusion broadens the operationally relevant distribution in the logarithmic Schmidt-rank coordinate on the scale $t^{1/4}$ and increases the amount of entanglement that can be borrowed. Charge transport therefore continues to reorganize the entanglement spectrum and activate embezzlement after the leading volume-law entropy has saturated.

We theoretically investigate the role played by non-Markovianity in the charging of a quantum battery. We focus on the case of a Micromaser, where the energy is stored in a resonant cavity mode and memory effects are introduced and controlled by coupling this mode to a memory ancilla, described as a two-level system, that in turn sequentially interacts with a stream of two-level chargers through pairwise exchange interactions leading to a partial swap. Through numerical analysis, we show that non-Markovian memory effects act as a resource that enhances both the charging capacity and the stability of this device with respect to the Markovian counterpart. We conclude our study showing that the proposed scheme can be implemented in state-of-the-art solid-state platforms for circuit quantum electrodynamics.

Differential equations can be encoded as ground-state problems by constructing a positive-semidefinite effective Hamiltonian whose minimum-energy state represents the solution. We extend this framework in several directions. First, we show how multiple nonzero initial, boundary, and data conditions can be incorporated into the homogeneous formulation $A | f\rangle=0$ using a known nonzero reference condition. We then analyse an alternative formulation based on $A |f\rangle = | b\rangle$, with Hamiltonian $H_b=A^\dagger(I-|b\rangle\langle b|)A$, which incorporates source terms and nonzero constraints through an augmented system. For nonlinear differential equations, we examine the unphysical ground-state degeneracy introduced by tensor-product representations and consider both Hamiltonian constraints and ansatz-level restrictions for targeting physically valid product states. Finally, we develop grid-value amplitude-encoded versions of both Hamiltonian constructions and compare them with spectral coefficient encoding. Through linear and nonlinear examples, we assess how the choice of Hamiltonian formulation and function representation affects solution recovery, spectral gap, degeneracy, and readout. These results broaden the applicability of ground-state-based quantum differential-equation solvers while clarifying their principal practical trade-offs.

We construct the first type of non-Euclidean non-autoregressive neural quantum state (NQS) in the form of the hyperbolic Restricted Boltzmann Machine (HRBM), which is studied in the variational Monte-Carlo (VMC) setting of the Quantum Sherrington-Kirkpatrick (QSK) model whose ground state exhibits volume-law entanglement. Across a 512-fold increase in the Hilbert space dimension corresponding to a system size increase from $N=14$ to $N=24$, HRBM NQS robustly outperforms its Euclidean version, the RBM NQS, in terms of better ground state energy optimization as well as lower Renyi-2 $S_2$ and von Neumann $S_{vN}$ absolute entanglement entropy reconstruction errors. More importantly, for all QSK system sizes, HRBM NQS demonstrates a superior expressivity in faithfully reproducing the entire entanglement spectrum of the QSK model from the top eigenvalues down to the tail end across 15 orders of magnitude, while RBM NQS consistently overestimates the sub-dominant modes. This work furnishes a proof-of-concept demonstrating that hyperbolic non-autoregressive NQS ansatzë, thanks to the exponential volume of the hyperbolic geometry underlying their constructions, might be more natural at representing volume-law quantum systems than conventional Euclidean NQS. Furthermore, an interesting byproduct of this work is the polynomial scaling result of RBM-type NQS ansatzë in the QSK volume-law system as the Hilbert space increases exponentially.

Quantum Amplitude Estimation promises to accelerate Monte Carlo integration by replacing the classical $\varepsilon \propto N^{-1/2}$ sampling law with the Heisenberg-limited $\varepsilon \propto N^{-1}$ scaling, but whether any part of that advantage survives on present-day hardware is an empirical question. We report a systematic experimental benchmark of a Maximum-Likelihood Amplitude Estimation QMC pipeline on IonQ trapped-ion processors, comprising 60 hardware trials on IonQ Forte-1 across five settings(5 & 9 qubits, 100-200 shots per depth, linear & exponential amplification schedules, ~113 device-hours), together with 100 trials on IonQ Aria-1 & Forte-1 noise models at 5, 9 & 19 qubits. The pipeline combines controlled-$R_y$ rotational state preparation, Grover-based amplitude amplification and maximum-likelihood inference and is benchmarked against $b_{\max}^{-1}\!\int_0^{b_{\max}}\!\sin^2\!x\,\mathrm{d}x$ with $b_{\max}=π/5$ ,given results emerge. First, the noiseless limit it attains $\varepsilon \propto N^{-0.88}$, close to the Heisenberg-scaling reference, reducing the error 54-74x over a 133x increase in oracle calls. Second, scaling does not survive on hardware. Every noisy backend saturates at an error floor of (2-5)x 10^{-2}, with fitted exponents of 0.04-0.15 on Forte-1 linear schedules and $α\le\!0$ on the vendor noise models: beyond the optimal shallow depth, however, deeper amplification provides no sustained accuracy gain and instead returns to the noise floor. Forte-1 hardware also outperformed IonQ's own Aria-1 noise model at every depth $m \ge 2$, indicating that vendor noise models are bad predictors of MLAE accuracy. The practical implication for UQ is that on current devices the useful operating point is a shallow, schedule-tuned amplification depth chosen so that the deepest circuit lands near p~1/2 not the deepest schedule the coherence budget allows.

We consider the simultaneous estimation of multiple parameters in Hamiltonians of the form $H_{\vecθ}= H_{\vecθ}^P + H^C$, where $H_{\vecθ}^P$ encodes the unknown parameters and $H^C$ is a control term. We consider three basic paradigmatic frameworks for metrology: (i) dynamical, where the parameters are encoded unitarily, (ii) thermal, and (iii) ground state. We generalize previous bounds for single-parameter estimation to simultaneous multiparameter estimation for all three metrological settings and establish the conditions required for their saturability. We then focus on vector magnetometry, deriving tight bounds for the simultaneous estimation of magnetic-field components and identifying optimal many-body control Hamiltonians $H^C$ that saturate them. These results establish the fundamental limits of vector magnetometry for unitary dynamics, thermal equilibrium states, and ground states.

Quantum circuit optimization replaces a circuit with an equivalent one of fewer gates and lower depth, reducing execution cost and error rate. We ask whether a generative model can learn this transformation directly from examples, rather than selecting from a fixed rewrite library or rigid algebraic routines. We present Bridge of $Ψ$'s (BOPS), a generative model based on Schrödinger bridges, using a custom denoiser architecture, that learns a transformation from a source circuit into an equivalent optimized circuit. We train it on data constructed to be hard for existing optimizers, by applying rewrite rules backwards so that each input has a known lower-cost target. On held-out 8 qubits $\times$ 64 depth Clifford+$T$ circuits, BOPS reduces gate count by $2.46\times$ and depth by $2.45\times$ in geometric mean, outperforming all nine baseline optimizers. This constitutes the first generative model bridging quantum circuits and frontier machine learning methods, opening up the quantum compilation stack to learned optimization along multiple axes.

We demonstrate spin--orbit-coupling (SOC) catalysis of magnetization-sector transfer in the half-filled Fermi--Hubbard model. Without SOC, conservation of total magnetization confines the dynamics to the initial sector, preventing an antiferromagnetically correlated state from reaching the polarized ferromagnetic sector under a Zeeman ramp. A transient SOC control lifts this obstruction by coupling otherwise disconnected magnetization sectors and converting symmetry-protected crossings into avoided crossings, thereby opening a finite-gap pathway for magnetic-state conversion. We further accelerate the SOC-enabled dynamics beyond the adiabatic timescale using gradient-ascent pulse engineering (GRAPE) and a variational quantum circuit. Both approaches achieve rapid magnetization transfer in one- and two-dimensional Fermi--Hubbard lattices. Our results establish transient SOC as a controllable catalyst for overcoming symmetry-imposed dynamical constraints, while optimal control sets the timescale for the resulting magnetization-sector transfer.

We prove that deciding the Berry phase for parameterised 2-local qubit Hamiltonians is BQP-complete when presented with a classical description of a guiding state, promised to overlap with the ground state of the system. Our results extend to systems with weighted Heisenberg interactions and when restricted to a 2D square or triangular lattice geometry. The techniques we develop leverage the Schrieffer--Wolff transformation, typically used in the construction of perturbative gadget reductions for local Hamiltonian problems, extending it to parameterised families of Hamiltonians. We demonstrate that there exists a choice of parameterised simulator Hamiltonians whose Berry phase well-approximates that of a parameterised target family. Using the perturbative gadget reduction framework of Oliveira and Terhal and of Schuch and Verstraete, we adapt the arguments to parameterised interactions and demonstrate the error bounds in the resulting simulation can be controlled. Additionally, we provide an explicit proof that families of 1-local Hamiltonians have a Berry phase that can be efficiently computed to inverse-polynomial precision. This establishes a complexity transition between 1-local and 2-local Hamiltonian families.

Imperfect photon sources degrade the performance of interference-based linear-optical entangling gates. We derive a universal fidelity law for these gates in terms of two standard source metrics: Hong-Ou-Mandel visibility and second-order coherence. We model the multiphoton component as an arbitrary overlap between noise and signal photons. While different values of the signal-noise overlap produce different error structures, associated with different physical platforms, all result in the same fidelity law. We test the model on our actively synchronized CNOT-gate experiment and against published results across different platforms, with no free parameters. This framework turns source characterization into a unified benchmark for photonic quantum computing.

Measurement and classical randomness usually degrade coherence; controlling where and when a subsystem is monitored can instead make them a tunable resource. We introduce a photonic time-multiplexed quantum walk whose fast reconfigurability enables precise position measurements, allowing us to study this interplay in a hybrid quantum-classical pursuit problem: A quantum walker (lamb) evolves on a line while a classical pursuer (lion) performs a lazy random walk. Each lion trajectory drives a distinct coherent, norm-reducing evolution of the lamb, with capture implemented by measurements at the lion's positions; averaging over the recorded trajectories then synthesizes a decoherent process. Counterintuitively, increasing the lion's mobility does not monotonically suppress survival: over a broad range of hopping probabilities, the lamb survives better than against an immobile predator. Directly observing this local enhancement, we demonstrate a manifestly quantum feature aided rather than hindered by classical stochastic control.

We introduce a nullspace-guided adaptive (NGA) bootstrap method that improves the energy lower bounds of quantum many-body ground states by refining the bootstrap basis in a dynamic and incremental way. At each iteration, the optimized moment matrix reveals a nullspace of saturated positivity directions, which is intuitively interpreted as annihilators of the approximate ground-state subspace. The NGA bootstrap then prunes operators with small nullspace leverage and grows the basis along descendants of these null directions. By applying the NGA bootstrap to the transverse-field Ising chain, we obtain nearly exact energy lower bounds because the algorithm automatically discovers the eigenoperator structure in terms of Jordan-Wigner fermions from a minimal local bootstrap basis. For the Hubbard chain, it improves upon state-of-the-art energy lower bounds by up to two orders of magnitude, reaching errors ranging from $10^{-3}$ down to $10^{-5}$ in the strongly correlated regimes. We further show that the NGA framework can be used to improve the certified two-sided bounds on general observables. In addition, the bootstrap error decreases approximately as a power law with increasing computational resources. These results suggest that our method provides a practical and scalable route toward accurate bootstrap of general quantum many-body systems.

Trapdoor claw-free functions (TCFs) underpin much of classical-quantum cryptographic interaction, yet every TCF-based protocol states its guarantees relative to an honestly generated key. We give a family-agnostic abstraction of key certification for (noisy) TCF constructions, built on two notions: a certifiable key relation, an NP relation capturing a family's honest keys with witnesses recoverable from the trapdoor; and certified key generation, which emits with each key a certificate of membership satisfying completeness, certificate soundness with extractability, and key privacy. We instantiate certifiable key relations for different constructions, each met generically by a zero-knowledge argument of knowledge for the relation. As our main application, a generic compiler turns any TCF-based proof of quantumness into a zero-knowledge one, with each security property following from its counterpart in the certification scheme. Finally, we delimit the primitive's reach: for protocols resting on injective invariance, an accepting certificate is itself a family distinguisher, leaking exactly the bit such protocols must hide.

A boolean function $f$ has Fourier dimension $k$ if its nonzero Fourier coefficients span a subspace of dimension $k$. We consider the property testing task of determining whether a function has Fourier dimension at most $k$, or is $ε$-far from being so. We show that there is a $Θ(k)$ quantum property tester for this problem. With Gopalan \etal's classical lower bound of $Ω(2^{k/2})$ for this task, this demonstrates an exponential quantum advantage for this task. We complement this result with a $\tilde{O}(2^{k/2}/ε)$ classical tester, improving the best known upper bound and thus showing the prior lower bound is essentially tight.

Device-independent quantum key distribution (DIQKD) can guarantee security without trusting the internal workings of the measurement devices, but extending it to fiber networks demands high-quality entanglement, reliable heralding, and faithful photon transmission simultaneously. Here, we address these requirements in an event-ready asymmetric atom-photon architecture implemented over $25\,\mathrm{km}$ of spooled telecom fiber. A single trapped $^{40}\mathrm{Ca}^{+}$ ion forms one party of the protocol while a single transmitted photon measured at the remote station forms the other. Double quantum frequency conversion and active polarization stabilization preserve the atom-photon quantum correlation across the full link. We obtain a Clauser-Horne-Shimony-Holt parameter of $|S|=2.75^{+0.16}_{-0.15}$, exceeding the threshold $|S|=2.362$ required for a positive asymptotic secret-key fraction under the DIQKD model used. Within the same asymptotic model, this corresponds to a conservative estimate of 69 secret-key bits out of 10908 detected Bell states. The demonstrated architecture establishes a route towards DIQKD in heterogeneous, repeater-compatible quantum networks.

Photon statistics provides a new control dimension for strong-field bound-state formation. Using a quantum-optical phase-space formulation coupled to time-dependent Schrödinger-equation calculations, we show that field fluctuations enhance multiphoton Rydberg excitation by broadening AC-Stark-shifted resonances, but suppress tunneling-mediated recapture even as ionization increases. A quantum-statistical recapture model attributes the latter to ensemble-induced dispersion of relative path phases. Photon statistics also reshapes Rydberg-manifold parity, linking field statistics to recapture coherence and final-state symmetry.

We establish exact thresholds for the failure of simultaneous quantum typicality: three parties for mixed states and four for pure states. For the four-qubit Higuchi--Sudbery state, every sequence satisfying the expected purity bounds on three overlapping marginals, with sufficiently small fixed positive entropy slack, is asymptotically perfectly distinguishable from the tensor powers of the input: its trace distance from them tends to the maximum value $2$. This maximal separation persists, with a common positive slack, throughout an open neighborhood in the full four-qubit state space. Tracing out one party yields a mixed tripartite example. The proof connects simultaneous quantum smoothing with polynomial concentration on $\CP^1$. Symmetry reduces the problem to a frame inequality on $\Sym^n(\mathbb C^2)$, where a linear entropy deficit competes with a quadratic cost of polynomial concentration. Bernstein--Markov estimates and a subharmonic barrier control this cost, yielding an exponential obstruction to simultaneous typicality. These results disprove Dutil's multiparty quantum typicality conjecture, formulated in 2011, and the one-shot simultaneous min-entropy-smoothing conjectures of Drescher--Fawzi and Colomer--Winter. Together with the positive results for smaller systems, they determine the smallest numbers of parties at which simultaneous typicality can fail.

The sensitivity of an atomic spin sensor is fundamentally constrained by the quantum Fisher information (QFI) of the probe state. The pinched state, $|{F,0}\rangle$, has an $(F+1)$-fold larger single-particle QFI for transverse-field sensing than the stretched state, $|{F,F}\rangle$, corresponding to a predicted $\sqrt{F+1}$ reduction in the spin-projection-noise-limited field uncertainty. We show that this advantage can be accessed in an rf sensing scheme by engineering a spectrum symmetric about $m=0$, yielding an ideal $(F+1)$-fold enhancement of magnetic-field response. For $^{87}\mathrm{Rb}$ with $F=2$, we observe up to 2.7-fold response enhancement. Implementing this approach in a compact $0.8~\mathrm{cm}^3$ anti-relaxation-coated multipass cell, we realize a single-beam, dual-axis, zero-field magnetometer, achieving $13$--$23$~$\mathrm{fT}/\sqrt{\mathrm{Hz}}$ over $3$--$100$~Hz at room temperature.

Quantum batteries are quantum systems that store useful energy, which can subsequently be extracted to perform work. In this work, we investigate the charging dynamics under continuous measurements and post-selection-based non-Hermitian quantum battery realized by a three-level system. By post-selecting the trajectories with no quantum jump $|1\rangle \rightarrow |0\rangle$, the dynamics is effectively confined to a two-level manifold. We analyze the resulting charging dynamics under both $σ_x$- and $σ_y$-driving protocols and investigate the roles of detuning, coherent driving, non-linearity, and measurement backaction. The generation and dynamics of quantum coherence, which plays a pivotal role in quantum battery, are also analyzed under post-selection. The advantage and comparison of our results over those of a generic two-level system and with Lindblad dynamics are also highlighted. Our work explores the interplay between the measurement axis and the driving protocols that govern the charging rate, ergotropy, and quantum coherence of the non-Hermitian, highly tunable, and controllable quantum battery.

We construct an oracle relative to which $\mathsf{BQP} \not\subseteq \mathsf{IP}$, resolving a long-standing open question in quantum complexity theory. Together with recent work due to Aaronson et al., our work also gives the first oracle separation between $\mathsf{IP}$ and $\mathsf{MIP}$, answering a question dating back to Fortnow's thesis. Our separation is based on the Forrelation problem, where given Boolean functions $f$ and $g$, the goal is to determine if $f$ is correlated with the Fourier spectrum of $g$. While this task is solvable by a query-efficient quantum algorithm, we show that it admits no classical interactive protocol with polynomial communication and a polynomial-query verifier. Our proof is based on (i) a new structural result showing how to approximate Avg-Max circuits (which are well-known to capture the power of interactive proofs in the oracular setting) by convex functions with small first and second derivatives and (ii) a novel analysis establishing that the Forrelation distribution suggested by Aaronson and Ambainis fools such functions. Our results imply that any prover-efficient classical interactive protocol for $\mathsf{BQP}$ must rely on non-relativizing techniques. This might serve as a partial explanation for the lack of progress towards doubly-efficient, unconditionally sound classical verification of quantum computation.

In classical systems, rugged potential energy landscapes provide a transparent mechanism for the celebrated Mpemba effect, in which hotter initial states cool down faster. This picture generally does not survive in quantum systems. Here we show how to design a quantum energy landscape with local dissipation leading to an Mpemba effect with parametrically separated timescales. Our approach uses Stark localization to design an energy landscape and localized incoherent hopping as cooling mechanism. The hops are triggered by rare "detection" events whose rate grows with energy, allowing hotter states to cool faster and producing super-exponentially separated cooling rates for localized initial states. We further show that the effect is dramatically enhanced by collective hopping of bound pairs in the presence of attractive on-site interactions. These findings have clear experimental signatures accessible in present-day setups.

We establish quantitative entropy contraction bounds for finite-dimensional quantum channels beyond detailed balance. For channels compatible with a faithful conditional expectation, we show that GNS (Gelfand--Naimark--Segal) norm contraction yields relative entropy contraction with only a logarithmic loss in the dimensional constant. For quantum Markov semigroups with a faithful asymptotic conditional expectation, this gives a lower bound on the complete modified logarithmic Sobolev constant in terms of the GNS spectral gap. The bounds allow initial entanglement with an external environment and are independent of its system size. Applications to alternating reservoir pulses and continuously coupled energy ladders give bounds with optimal size dependence.

Heralded multipartite entanglement distribution is a key requirement for device-independent conference key agreement (DI-CKA) over lossy quantum networks. Although locally equivalent in the absence of loss, different single-rail photon-number encodings of Greenberger-Horne-Zeilinger (GHZ) states can exhibit substantially different loss tolerance. We show that computational-basis GHZ states, comprising a coherent superposition of vacuum and an $n$-photon component, enable detection-loophole-free parity-CHSH violations at markedly lower detection efficiencies than previously considered fixed-photon-number GHZ states, and derive exact analytical conditions for the critical detection efficiencies of both state classes. Motivated by this advantage, we introduce a star-network protocol using heterogeneous sources to directly herald vacuum-$n$-photon GHZ states with long-distance scaling $O(η_{\mathrm{c}}^{n/2})$, where $η_{\mathrm{c}}$ is the channel transmittance. For four users, we characterize the heralded state under photon loss and show that tunable source parameters preserve genuine multipartite entanglement at any finite channel distance. For both ideal Pauli measurements and experimentally accessible displacement-based measurements, our protocol enables DI-CKA at detection efficiencies achievable with current photodetectors, while retaining key rates and communication distances comparable to those of previous heralded schemes. We discuss physical implementations and analyze an SPDC-based realization, showing that source-induced asymmetry can make measurement-role assignment in the parity-CHSH test crucial. These results identify photon-number encoding, source architecture, and measurement-role assignment as design parameters for loss-tolerant multipartite quantum networks and enhanced DI-CKA performance.

High-fidelity two-qubit gates in neutral-atom arrays rely on the Rydberg blockade, which is intrinsically short ranged and requires long range connectivity to be achieved through atom shuttling. We propose a four level architecture, where the typical ground state qubit can be leveraged for its long lifetime and the Rydberg states couple to a microwave cavity, allowing for long range cavity mediated gates. We first find the thermal dependence of two established protocols, the dispersive iSWAP native to the Tavis-Cummings model and the Controlled phase gate generated from driving the cavity. We simulate them under the presence of Rydberg decay, thermal photons, finite cavity linewidth and find fidelities which accompany closed form bounds. We then introduce the bichromatic Raman gate, which only virtually populates the Rydberg states and cancels dispersive shifts to mitigate both atomic and cavity decay, achieving a fidelity of $F = 0.997$. Finally, we consider a full optical tweezer array in a microwave cavity, and show that using a cavity mediated gate to close the periodic boundaries of the toric code shortens an error correction round by a factor of 2.3 for realistic array sizes. This was then applied to the wider family of Bivariate bicycle codes, and we find that it shortens a round of the gross code by a factor of 4.8.

Fisher-information-based optimization of programmable optical front ends in situ generally requires a response model or parameter-labeled measurements. We show that natural parameter fluctuations can instead provide the training signal. We construct proxies for the Fisher information (FI) of one parameter and the prior-weighted FI spectrum of multiple parameters from measured covariances after subtracting conditional detection noise, assuming locally affine responses. We use simulated photon counts from two incoherent point sources to train a mode sorter that approaches the quantum limit for separation and the Nagaoka--Hayashi single-copy bound for joint centroid--separation estimation. We demonstrate count-only updates that require no instrument response model and achieve performance comparable to model-based gradients. Our results provide a route to adaptive optical measurements without controlled parameter scans.

In cavity optomechanics, the standard large-detuning regime is commonly described by retaining only the radiation-pressure interaction, while higher-order mirror--field interactions are assumed to be negligible. This approximation, however, fails to provide a microscopic explanation for the vacuum-mediated heat transfer observed between the mechanical membranes in the experiment of Fong, et.al.,[Nature \textbf{576}, 243 (2019)], whose physical origin has remained under active debate. Here, using a fully quantum model, we show that the neglected higher-order optomechanical interactions naturally generate phonon-phonon coupling and quantitatively account for the observed energy exchange within the standard optomechanical framework. Building on this microscopic description, we further propose a protocol in which phonon-phonon interaction drives a cyclic process enabling net work extraction. Our results establish the fundamental role of higher-order optomechanical interactions and provide a microscopic framework for describing next-generation optomechanical experiments beyond the linear approximation.

Trapped ions excited to high-lying electronic states, so-called Rydberg states, open new opportunities for quantum simulation and quantum computing. Generally, the fidelity of quantum coherent operations critically depends on the longevity of Rydberg states. However, scaling laws predict that the lifetimes of Rydberg states in singly charged alkaline-earth metal ions are 16 times shorter, compared to their neutral atom counterparts. Here, we show that this is not generally the case. We report an anomalous lifetime enhancement of certain low angular momentum ionic Rydberg series by factors larger than eight. The anomaly is present at both zero and finite temperature, although it is caused by different mechanisms. At zero temperature, the anomalously enhanced lifetimes are caused by accidental cancellations of the relevant dipole transition matrix elements, while at room temperature the anomaly originates from the enlarged energetic separation of ionic Rydberg levels with respect to neutral-atom levels.

We present a theoretical proposal for measuring correlation functions in a quantum field system based on the use of quantum quenches. Using the examples of massive and massless scalar field theories, we show that a short-term perturbation of the system leads to a dependence of the further evolution of the average field on the initial state's correlation functions. Considering two types of perturbations, namely local and nonlocal quenches, we show which correlation functions can be measured in each of these cases. The proposed procedure can be applied to study non-Gaussian correlations.

Quantum emitters such as semiconductor quantum dots can provide entangled photon pairs emitting from a system of cascaded states. However, the resulting temporal correlation between the two photons from the three-level ladder system has been shown to set a limit on the achievable two-photon interference. In this work, we show that such limitation, for photons emitted by the second transition, is only due to reduced temporal overlap at the interference beam splitter. We investigate this theoretically and experimentally by determining time-resolved four-photon coincidences between two successively emitted photon pairs. Post-emission synchronization shows the recovery of maximum interference visibility; in prospective quantum networks this could be achieved via deterministic quantum memories.

Entanglement and Bell nonlocality have different sharing constraints across subsystems of a multipartite quantum system. We examine simultaneous violations of Bell inequalities with two-outcome observables and two or three measurement settings per party. We identify configurations whose simultaneous violations can be demonstrated on IBM Quantum hardware, and derive bounds and trade-off relations for several polygamous configurations. The results connect experimental capabilities of quantum computers with mathematical methods for studying the limits of quantum correlations.

In non-equilibrium probes, quantum-enhanced sensitivity is quantified through super-linear scaling of precision with respect to time, as a central metrology resource. However, this requires optimal measurements, which are often complex and time-dependent, making it challenging in practice. Sub-optimal measurements typically fail to retain robust super-linear scaling and show oscillations. Here, we begin by establishing a universal temporal scaling law in a general multi-parameter non-equilibrium quantum sensing framework. Within this setting, we identify the universal behavior of the sensing precision with sub-optimal measurements which shows quadratic scaling modulated by an additional bounded oscillatory function. To remove the oscillatory part, we propose a protocol in which measurements are partitioned into different groups, each performed at different times. The collective precision obtained from this protocol stabilizes a robust quadratic scaling even for sub-optimal measurements in the multi-parameter regime. We validate our protocol through three distinct examples as well as Bayesian estimation. Our protocol is applicable to every informative measurement and takes a key step towards practical realization of quantum-enhanced sensitivity.

Solid-state frequency standards are generally limited by strong decoherence, rendering conventional interrogation schemes inefficient. The $^{229}$Th nuclear clock provides a unique and timely platform for solid-state optical metrology and nuclear cavity quantum electrodynamics (QED), featuring a coherence time many orders of magnitude shorter than the radiative lifetime in current experiments. Here, we propose and analyze three cavity QED-enhanced clock interrogation schemes that turn this timescale mismatch into an advantage, leveraging collective coupling of thorium nuclei to nanophotonic modes to enable fast interrogation and detection despite the long population lifetime. We reveal the central role of collective cooperativity in determining the clock frequency instability, and derive the optimal conditions (power, working-point detuning, thorium density) for clock operation.

Standard variational quantum simulation seeks to reproduce the evolution of the full quantum state, although many applications require only the expectation values of a few observables. We study a variational method for pure-state Hamiltonian dynamics that updates circuit parameters to reproduce the evolution of selected expectation values. An exact error identity guides the choice of observables, motivating a construction based on repeated commutators of the target with the Hamiltonian. For Pauli observables and Pauli-rotation circuits, the update can be estimated without ancillary qubits or controlled operations for overlap estimation. Across six-qubit spin, fermionic, and molecular benchmarks, the targeted update extends the median time within the target-error tolerance by up to a factor of $4.2$ relative to standard variational quantum simulation at equal shot budgets. These results show that directing the variational update toward the target observable can extend accurate simulation without increasing the measurement cost per time step.

Altermagnets, characterized by vanishing net magnetization and momentum-dependent spin splitting, provide a promising platform for next-generation Josephson devices. Here, we exploit the Josephson effect in superconductor-altermagnet-superconductor junctions and show how to engineer prescribed current-phase relations by device design. Based on these programmable Josephson potentials utilizing altermagnetism, we propose a new class of transmon-like superconducting qubits that combine large anharmonicity with enhanced robustness against decoherence via coherent two-Cooper-pair tunneling. We show that in the $2φ$-junction regime, this kind of qubit provides intrinsic protection against charge noise due to parity protection. Magnetic flux can be used to precisely control the qubit and, under appropriate bias, this architecture further suppresses charge and flux noise. Our results establish altermagnets as a versatile platform for Josephson-potential engineering and open a new route toward high-performance superconducting qubits combining high coherence, large anharmonicity, and broad tunability.

Neutron and X-ray perfect-crystal interferometers (PCIs) are powerful platforms for studies of fundamental physics and phase-contrast imaging. Further enhancing several PCI capabilities requires reducing crystal blade thickness to the micron scale, which minimizes dynamical-diffraction image blur, permits operation in the pendellösung regime where blade thickness controls beam splitting, and reduces absorption for simultaneous neutron and X-ray operation. However, fabricating multiple crystal blades with identical micrometer-scale thicknesses over centimeter-scale areas remains a major challenge. Here, using a non-etching sub-micron fabrication technique, we demonstrate silicon triple-Laue interferometers with equal-blade-thicknesses of 110 $μ$m and 350 $μ$m, operated with both neutrons and X-rays. These devices are the thinnest PCIs realized to date, enabling a factor-of-six reduction in dynamical-diffraction beam spreading for improved phase-contrast imaging, while reaching the single pendellösung length regime in which crystal thickness provides an experimentally accessible control parameter for engineered quantum-optical beam splitting of plane-wave inputs. These results motivate multi-blade PCI designs utilizing identical half-pendellösung crystal lamellae that are proposed for neutron spin--orbit and electric dipole moment measurements.

The notion of a spatiotemporal quantum state extends the conventional concept of a spatial quantum state to the spatiotemporal domain. Such states are represented by unit-trace operators that encode correlations among quantum events distributed across space and time. In this work, we use the spatiotemporal Kirkwood-Dirac phase space to provide a unified characterization of spatiotemporal quantum states. Spatiotemporal states obtained from Kirkwood-Dirac distributions are generally non-Hermitian and nonnormal; whereas those constructed from Margenau-Hill distributions are Hermitian. We provide a unification via (quasi)probabilistic mixture of Kirkwwod-Dirac spatiotemporal states which encompasses almost all existing formulations of spatiotemporal quantum states. We derive recursive expressions for spatiotemporal states and elucidate the relation between Kirkwood-Dirac nonclassicality and the temporality of spatiotemporal states. We further extend the construction to many-fold correlation functions and establish its connection with out-of-time-ordered correlators (OTOCs). We also develop a more general unifying framework based on (quasi)probabilistic mixture of $s$-parametrized spatiotemporal states and establish their Petz time reversal and application in studying Kubo-Martin-Schwinger (KMS) condition in two-time setting. Finally, we apply this framework to characterize quantum entanglement in spacetime and analyze spatiotemporal entanglement using several complementary entropy measures.

The Wigner entropy conjecture posits that pure Gaussian states minimize the Shannon entropy of non-negative Wigner functions, known as the Wigner entropy. We show that mixing a specific pure Wigner-negative state with another suitably chosen quantum state can restore Wigner positivity while retaining a Wigner entropy that is slightly - but strictly - below the vacuum entropy. As a consequence, we disprove the Wigner entropy conjecture, as well as the stronger Wigner majorization conjecture, by deriving simple analytical counterexamples with violations of the entropy bound no larger than $10^{-3}$. Such states with sub-vacuum Wigner entropy can be found arbitrarily close to the vacuum and can also exhibit sub-vacuum Wigner-Rényi $α$-entropy for $0<α<2$. We identify the physical mechanism behind the existence of such states, which arises from a subtle interplay between the uncertainty principle and non-Gaussianity. The key idea of this paper was developed with the help of AI tools, building on the characterization of extreme non-negative Wigner functions.

Quantum machine learning is a promising paradigm for learning from limited data, a central bottleneck in domains such as medical imaging, clinical trials, and rare diseases. Quantum convolutional neural networks (QCNNs) are particularly attractive in this setting, combining a hierarchical architecture with strong inductive bias and a parameter count that grows only logarithmically with system size. Their appeal rests on the generalization bounds of Caro et al. (2022), which show that the generalization error of a quantum model scales with the number of trainable parameters rather than with the Hilbert-space dimension, placing QCNNs in a potentially sample-efficient regime. We develop a hardware-compatible QCNN with mid-circuit measurement and classical feed-forward, and show on a binary handwritten-digit task that strong test performance is achievable from as few as 10 training samples, with the generalization error decreasing as the training set grows. At a matched 45-parameter budget the QCNN learns where an equally small classical convolutional network stays at chance, although an unconstrained classical baseline with roughly 25,000 parameters remains strongest when data are plentiful. Transpiling amplitude and angle encoded circuits across image resolutions from 2x2 to 512x512 pixels then exposes the dominant scaling bottleneck: amplitude encoding stays qubit-efficient but grows extremely deep, whereas angle encoding stays shallow but becomes qubit-prohibitive. On the medically motivated BreastMNIST benchmark the QCNN does not surpass the unconstrained classical network, yet it learns consistently above chance using orders of magnitude fewer parameters. Our results indicate that for QCNNs, learning from few samples is attainable in practice, whereas scaling to realistic image data is constrained less by optimization than by data encoding and hardware execution.

Language models can be adapted by changing the computations applied to individual tokens. Quantum circuits offer one such approach, but evaluating wider circuits inside a large model can be computationally demanding. Here we introduce HyperQ, which adds token-conditioned quantum residual branches to a frozen masked-diffusion language model. A quantum residual branch is a module in each transformer block that reads a token's hidden state, emits the coordinates of that token's circuit, executes it, and adds the measured values back through a residual connection. The backbone remains frozen, and only the added branches are trained. Within each branch, a lightweight circuit hypernetwork emits token-specific rotation angles, coupling strengths, and measurement axes in a shared sparse circuit structure. The required expectation values have an exact classical expression whose evaluation cost grows linearly with the qubit count, enabling circuits from 16 to 64 qubits to be trained within a 1.1-billion-parameter backbone. Across downstream benchmarks, increasing circuit width raises the average score from 47.65 to 54.30. At 64 qubits, HyperQ exceeds the backbone and its low-rank-adapted counterpart by 4.71 and 3.67 points, respectively. HyperQ is fine-tuned on 20,000 prompt-response pairs, compared with 200,000 for the classical baselines. These findings support token-conditioned circuit emission as a tractable architectural approach to quantum-augmented language modelling.

Dynamical quantum phase transitions (DQPT) are commonly defined either by the behavior of a late-time order parameter or by nonanalyticities in a quantum state's return rate. We show that discrete phase space fundamentally separates these two notions by the scale of information they require. An order parameter transition is determined by a local reduced state, requiring no quasiprobability negativity. In contrast, general global returns can contain information absent from every proper reduced state. For stabilizer returns, we derive an exact decomposition of the rate into distinct costs from loss of support and destructive quantum interference. Dynamics of a qutrit Potts chain show that selective cancellation can reverse the ranking of competing block returns and delay their exchange. An exact control also exhibits a thermodynamic return cusp with zero negativity at the crossing. The existence of a return singularity and the role of interference in selecting its branches are therefore distinct physical questions.

Time ordering is a central obstacle in driven open-system dynamics governed by master equations with time-dependent rates. We derive explicit closed-form factorizations of the chronological and antichronological propagators for a time-dependent generator of the form $\mathcal{L}(t)=α(t)A+β(t)B$, when the commutator $[A,B]$ is a simultaneous eigenoperator of the adjoint actions of $A$ and $B$, namely $[A,[A,B]]=λ_{A}[A,B]$ and $[B,[A,B]]=λ_{B}[A,B]$. In contrast to the disentangling procedure known as the Wei-Norman decomposition, our construction determines the factorization coefficients directly, without solving a coupled system of nonlinear differential equations. Applying this result to the bosonic gain-loss Lindblad equation, we obtain the exact dynamical map for arbitrary time-dependent gain and loss rates. The gain-loss master equation provides a canonical description of a driven harmonic oscillator coupled to a thermal bath. We benchmark the construction by deriving the time evolution of the Wigner function of an initial Fock state and comparing it with independent phase-space results. We further apply the resulting dynamical map to evaluate the code-space survival probability of a binomial bosonic code under driven gain-loss dynamics.

Molecular properties govern how molecules interact with one another or external fields. Accurate molecular properties are essential for constructing intermolecular interaction models, and to achieve high accuracy we need to go beyond leading-order (dipolar) terms. This work presents CCSD(T) references for 73 small non-spin-polarized molecules for molecular dipole and quadrupole moments, and dipole-dipole and quadrupole-quadrupole polarizabilities. Using these results, we provide a holistic performance analysis of molecular properties computed with HF, MP2, CCSD, and a wide range of density-functional methods. Additionally, we investigate in detail what levels of basis sets are required to simultaneously describe all properties in the data set. The best-performing density functionals for all four properties are the asymptotically cor- rected hybrid GGAs B97-3-AC, closely followed by PBE0-AC. Surprisingly, modern meta- GGAs and range-separated functionals perform inconsistently, with large errors in the quadrupo- lar properties. These results have direct implications for methods for intermolecular interac- tions, such as symmetry-adapted perturbation theory based on density functional theory, or for the quality of properties and interactions in machine-learning datasets. Finally, for DFT methods, the Jensen aug-pcseg-2 basis set is a computationally efficient alternative to more established basis sets, but for generating correlated references, third-row elements benefit from core polarization, and double augmentation is strictly necessary for quadrupole-quadrupole polarizabilities.

We develop an operator formulation of statistical quasiparticle theory for open quantum systems with nonlinear system-bath coupling, extending beyond the linear coupling setting of the standard Gaussian influence functional formulation. For Gaussian baths, the statistical quasiparticles, termed dissipatons, are explicitly constructed as collective operators in the thermofield bath space. Our construction provides a microscopic operator basis for the dissipaton algebra and generates hierarchical equations of motion directly from the Liouville equation. Nonlinear interactions are incorporated through a recursive generalized Wick's theorem, enabling automatic generation of hierarchical equations for polynomial couplings. The resulting framework connects explicit bath operator representations to nonperturbative, non-Markovian dynamics and unifies the treatment of linear and nonlinear system-bath interactions.

The fact that generic isolated many-body quantum systems thermalize is understood using the eigenstate thermalization hypothesis (ETH). In recent years, there has been much interest in the behavior of the ETH spectral functions, which characterize the smooth dependence of the variance of the off-diagonal matrix elements of observables on the associated energy and frequency, and whose low-frequency part contains information about the long-time dynamics. In finite systems described by the ETH, the spectral functions are expected to exhibit plateaus below a characteristic frequency $ω^{}_{\mathrm{ETH}}$. In this regime, the statistics of the matrix elements of observables are expected to be described by random matrix theory. Related frequencies that have been studied in the literature are $ω^{}_{\mathrm{SFF}}$, which controls the onset of random-matrix behavior in the spectral form factor, and the transport frequencies $ω^{}_{\mathrm{tr}}$, which are derived from transport coefficients. However, a direct quantitative comparison of these frequencies is lacking. Using exact diagonalization, we conduct such a comparison for the spectral functions of current operators in clean and disordered quantum spin ladders with diffusive energy and spin transport. We find clear evidence for the expected low-frequency plateaus in the ETH spectral functions. For the accessible system sizes, $ω^{}_{\mathrm{SFF}}$ is consistent with the extent of the plateaus, while the transport frequencies are systematically larger and lie in the nonuniversal regime of the spectral functions. Our findings highlight the need to better understand the origin of these quantitative differences.

We introduce the superconducting Talbot effect---a macroscopic quantum self-imaging phenomenon occurring when proximitized Cooper pairs propagate through a ballistic two-dimensional electron gas. By configuring periodic superconducting leads into a phased-array Josephson junction with programmable phase differences, we demonstrate active steering of the resulting superconducting Talbot carpet. To overcome transport resolution limits, we design a Vernier-scale collector array that performs sub-wavelength sampling of the fractional Talbot pattern. This approach maps real-space quantum interference with high robustness to disorder, enabling direct extraction of Fermi wavelengths across helical, spin-degenerate, and spin-orbit-split Fermi surfaces. Tight-binding numerical calculations on a square lattice validate the real-space interference patterns. Our results establish a versatile framework for coherent wavefront engineering and quantum materials diagnostics in superconducting optics.

Scaling quantum networks requires architectures extending end-to-end service reachability despite constrained fibre and equipment. Critically, in brownfield deployments, the quantum network must be engineered around classical telecommunications infrastructure and the operating capabilities of quantum key distribution (QKD) technology. To address this, we demonstrate a seven-node, multilayer QKD network deployed over existing metropolitan fibre. The implementation compares spectral management techniques to accommodate inherited constraints across its layers. It combines a trusted-node ring with a three-node subnetwork interconnected through reconfigurable optical switching, extending physical connectivity and service reachability without an additional transmitter. A meshed key management layer maps endpoint requests onto trusted-relay paths and supplies Layer 1, Layer 3, and one-time-pad applications. Over 73 days, eight link configurations generated 119.4 Gbit of secret key material with 99.1% link availability. Randomised end-to-end requests revealed indirect cross-layer coupling between key consumption, stored-key state and quantum-layer reconfiguration, demonstrating resource sharing through reconfigurability, spectral multiplexing and logical key-management abstraction.

For a single particle, a quantum information engine can turn measurement fluctuations into transport by raising a barrier behind the particle each time its position is measured. When many particles are present, the barrier still depends on just one number, the position of the leftmost particle, so we let the demon measure that order statistic and nothing else. A demon that resolves every position instead pays a record entropy that grows with particle number, even though the extra distinctions never change where the barrier is placed. We show that the coarser measurement supplies an energy that is bounded independently of particle number, and that this bound yields a ceiling on the record entropy that falls as the filling increases. At the same tilt, the collective engine then delivers $44\%$ more work per recorded nat than independent single-particle engines, each with its own optimized cycle time and each running at equal or greater power per particle. Pauli blocking ends this advantage once the accessible region just above the wall fills. We also evaluate the coherence that the coarse measurement leaves behind, and the cost of placing the barrier imprecisely.

We investigate multipartite entanglement in a particular family of pure $n$-qubit hypergraph states through a statistical-mechanics framework, where the average bipartite purity maps onto an effective Hamiltonian of $2^n$ classical binary spins. In this correspondence, each hypergraph state uniquely corresponds to a classical spin configuration, while temperature serves as a control parameter that continuously interpolates between a uniform ensemble of random hypergraph states at high temperature and maximally multipartite entangled states (MMES) at zero temperature. Remarkably, the exponential of the zero-temperature entropy directly gives the number of MMES within the set of hypergraph states. For small system sizes ($n \leq 5$), we perform an exact enumeration, fully characterizing the energy landscape and associated thermodynamic observables, and validating known MMES counts. For larger systems ($n = 6$ and $7$), where exact methods become computationally infeasible, we employ simulated annealing and parallel tempering algorithms to efficiently sample the exponentially large state space. Our analysis yields quantitative predictions of the number of MMES and reveals how entanglement is statistically distributed across the sets of hypergraph states. These results establish hypergraph states as an ideal platform for investigating multipartite entanglement through thermodynamic methods, offering both computational advances and physical insights into the structure of quantum entanglement in restricted families of quantum states.

Variational hybrid quantum models are a common paradigm for realising machine learning on quantum hardware. Nonetheless, they are challenging to train due to several problems intrinsic to the loss landscapes formed by variational quantum circuits. To mitigate these issues, researchers have extended the idea of subspace controllability leading to an increase in the success rate of variational models in finding the global minimum for quantum-based tasks. However, it remains unknown whether these results extend to classical-based tasks, and if any advantages are realised over a hyperparameter search. We begin to address this question by employing controllable circuits in a multi- classification task using MNIST-1D. Our results show that over a hyperparameter search, the majority of quantum models that achieve the lowest training and validation losses are subspace controllable. These results indicate that the hyperparameter search can be restricted to such models, in turn reducing computational cost and time.

We present a first-principles study of the electronic structure and thermoelectric properties of Zn-doped SnTe using the Korringa-Kohn-Rostoker method within the coherent potential approximation, complemented by pseudopotential calculations. SnTe is a lead-free analogue of PbTe and a candidate thermoelectric material in which Zn doping has been experimentally reported to enhance the performance of $p$-type samples. We show that Zn introduces a resonant-like impurity state, located within the conduction band, which evolves strongly depending on the Zn concentration. This feature leads to a significant enhancement of the thermopower in $n$-type SnTe. In the valence band, Zn doping induces L-$Σ$ band convergence, also resulting in an increased $p$-type Seebeck coefficient over a broad concentration range and delaying the onset of the bipolar effect. We further demonstrate that the Zn-induced band-structure modifications drive a transition from an inverted to a trivial band ordering, indicating a controllable topological phase transition. Our results clarify the microscopic role of Zn in SnTe and identify doping as a mechanism for simultaneously tuning thermoelectric and topological properties.

We investigate the harvesting of genuine tripartite entanglement by three linearly arranged Unruh-DeWitt detectors locally coupled to a massless scalar field in a gravitational wave background. We show that gravitational waves play a dual role in entanglement harvesting, either enhancing or suppressing the harvested entanglement depending on the system parameters. In particular, genuine tripartite entanglement exhibits a pronounced nonmonotonic response to the gravitational wave frequency, characterized by successive suppression, enhancement resembling resonance, and renewed suppression, while approaching its corresponding value in Minkowski spacetime in the regime of high frequencies. Its dependence on the detector separation is also nonmonotonic, displaying local enhancement peaks that are absent in the corresponding bipartite entanglement behavior. Compared with bipartite entanglement, genuine tripartite entanglement therefore exhibits a higher sensitivity to gravitational wave perturbations in both the frequency and spatial domains. These results suggest that genuine tripartite entanglement may provide a sensitive quantum probe of spacetime perturbations induced by gravitational waves.

We propose a protocol for extracting work from a coherent quantum battery state by exploiting measurement-assisted feedback mediated by a continuous-variable pointer. The scheme relies on the unitary operator $U = \exp(-i k t \, \hat{H} \otimes \hat{P}/\hbar)$, which generates entanglement between the battery's energy eigenstates and the position of an auxiliary pointer. A subsequent projective measurement of the pointer's position conditionally prepares the battery in a pure state from which work can be extracted via a feedback unitary. We analyze the protocol for a two-level quantum battery and a Gaussian pointer, computing the conditional states and the corresponding daemonic ergotropy. For the pure initial state considered, we find that the daemonic ergotropy equals the standard ergotropy for all interaction strengths, demonstrating that the measurement-assisted feedback recovers the full extractable work that would otherwise become inaccessible due to entanglement with the pointer when its degrees of freedom are traced out. The protocol thus provides a physically transparent realization of a quantum Maxwell demon, where the pointer acts as a quantum measurement ancilla whose position becomes correlated with the battery's energy. The scheme is amenable to experimental implementation in trapped-ion systems, and it contributes to the ongoing efforts to understand the role of quantum coherence and measurement in thermodynamics.

Integrated photonic microprocessors provide high-bandwidth, massively parallel linear computation, but realizing nonlinear feature maps and temporal memory remain key challenges for machine learning. Conventional approaches rely on active tuning and additional nonlinear elements, increasing architectural complexity and power overhead. Here we demonstrate an integrated photonic quantum reservoir computer that achieves nonlinear mapping, fading memory, and task versatility without active tuning of the reservoir core. The same chip supports accurate static classification, dynamic prediction, and stable autonomous forecasting, establishing broad utility across both classification and temporal inference tasks. Competitive performance is retained in the zero-bias state, where all on-chip phase shifters are unpowered, eliminating active control and reducing computational power consumption to zero. This passive operation highlights a scalable route to multifunctional machine-learning hardware, where large-scale photonic quantum processors can be repurposed as reservoirs without reconfiguring their internal optical networks. By combining quantum-state encoding, multimode interferometric mixing, and photon-statistical readout, this architecture provides a physically grounded paradigm for low-power, large-scale quantum reservoir computing.

We reduce Lalonde's pseudo-telepathy inner product game from six to five dimensions, keeping its four Alice questions and three Bob questions and reducing each answer alphabet to five. We prove that the reduced game self-tests its nonmaximally entangled state and all 35 measurement effects. The self-test is also robust: for a strategy winning with probability at least $1-\varepsilon$ we obtain $d_{\mathrm{ext}}\le\min\{1,2^{21}\sqrt{\varepsilon}\}$, where $d_{\mathrm{ext}}=\sqrt{1-Ξ}$ and $Ξ$ is the optimal squared fidelity with the reference state under local extraction channels. A compactness argument then gives simultaneous qualitative robustness for all measurement actions on the state under common local isometries. As a consequence of the self-test, no maximally entangled state of any finite dimension can win the game perfectly.

We study the asymptotic behavior of Shor's quantum factoring and discrete log algorithms when noise affects the precise controlled rotation gates in their quantum Fourier transforms. Improving the results of Cai (2024) and Cai and Young (2025), we identify a sharp and vanishingly small noise threshold. If the noise level lies below this threshold, then the two algorithms succeed in expected polynomial time. If the noise level exceeds this threshold, then the algorithms provably fail to solve their respective problems in expected polynomial time when the underlying primes belong to a set of positive density.

Annealing a semiconductor makes its vacancies mobile; they aggregate into multi-vacancy complexes that often carry spin. Such centres are a magnetic-noise source for any spin qubit among them, in silicon and silicon carbide as well as in diamond, and they are accordingly blamed for NV- decoherence in irradiated and implanted diamond, with two coherence records credited to removing them. Cluster-correlation-expansion simulations driven by published electron-paramagnetic-resonance parameters invert that attribution. At a fixed paramagnetic spin density a multi-vacancy bath gives a Hahn-echo coherence time 2.7-4.4 times longer than a bath of isolated negative vacancies, constant over three decades of concentration. A bath dephases the qubit because its spins exchange spin projections with one another, and two can exchange only if their transition frequencies match. A fine-structure splitting shifts those frequencies. Were every defect on the same crystallographic site, all would shift alike and still match: worth only a factor 1.3. Real defects occupy symmetry-equivalent sites pointing in different directions, so neighbours land at different frequencies and stop exchanging: a further 1.9. What governs the coherence time is therefore the fraction of bath pairs sharing a transition frequency, not the zero-field splitting. Vacancy aggregation extends NV- spin coherence rather than shortening it.

Understanding the entanglement cost of non-local quantum computation (NLQC) is relevant to complexity theory, cryptography, quantum gravity, and related areas. A central special case is $f$-routing, motivated in part by quantum position verification. Proving lower bounds on its entanglement cost in the fully robust setting has been a major open problem in NLQC. Motivated by this problem, we establish two related lower bounds. First, we study the shared-randomness cost of robust conditional disclosure of secrets (CDS). The connection between CDS and $f$-routing established by Allerstorfer et al. (Quantum 2024) makes understanding the randomness complexity of robust CDS a natural step toward lower bounds for the fully robust routing problem. We show that the shared-randomness cost of robust CDS is lower bounded by the logarithm of deterministic SMP communication complexity, even when communication and private randomness are unrestricted. Our lower bound is tight for the equality function. Second, we consider one-sided-perfect $f$-routing, in which the protocol is exact on one input class and has constant error on the other. By exploiting the positivity of the low-rank matrix arising in the method of Asadi, Culf, and May (ITCS 2025), we derive a general lower bound on the entanglement cost in terms of sign rank. In particular, this yields a linear lower bound on the entanglement cost of routing for the inner-product function in both one-sided-perfect settings, matching the known upper bound.

How spatial structures manifest in multi-time correlations is a fundamental question in turbulence. We develop a non-Hermitian bosonic framework that unifies equal-time anomalous statistics and their temporal propagation within a common operator representation. A continuous Wegner flow reorganizes stochastic mode couplings in an extended wave-frequency space. Applied to the Taylor-Kraichnan model, the framework recovers the established equal-time hierarchy and constructs multi-time contributions through propagators acting on successively smaller sets of active fields. This construction separates uniform transport from intrinsic relative dynamics and shows how a higher-order equal-time state evolves under a generator acting only on the fields that remain dynamically active. Within an isotropic radial closure, we derive an explicit fourth-order two-time zero mode scaling function that describe how relative dispersion progressively weakens sensitivity to the initial separation. The framework thus connects spatial intermittency to temporal evolution by identifying how the sequence of observation times determines the propagation of equal-time anomalous structures.

We present a gate-based quantum computing solution of the homogeneous Bethe-Salpeter equation (hBSE) for the bound state of two massive relativistic scalar particles interacting via ladder-approximation scalar exchange. After Wick rotation to Euclidean space and O(4) S-wave partial-wave projection, the hBSE is reduced to a symmetric matrix eigenvalue problem of dimension N = 2^n. We decompose the resulting Hamiltonian into a sum of n-qubit Pauli operators and solve it with the Variational Quantum Eigensolver (VQE) using a Matrix Product State (MPS) tensor-network ansatz. For N=16 (n=4 qubits), the VQE recovers the maximum eigenvalue - which encodes the minimum coupling constant for binding - to better than 1 % mean relative error compared to classical diagonalization. Entanglement analysis of the BSE amplitude shows low, area-law-like entanglement over the tested sizes, which motivates the MPS ansatz. A critical analysis of three independent barriers - exponential Pauli overhead, approximately size-independent low entanglement, and decreasing VQE gradient scales for the tested ansatz, consistent with generic barren-plateau concerns at larger n - reveals that the specific problem studied here lies in a classically tractable regime: over the tested range it is well described by low-bond-dimension tensor networks and efficiently handled by MPS/Lanczos methods. This negative result provides, to our knowledge, the first entanglement quantification of the BSE amplitude in qubit encoding, establishes the Pauli Hamiltonian framework for future BSE variants, and identifies 2D Minkowski-space BSE, N-body bound states, and non-ladder kernels as physically motivated extensions where genuine quantum advantage may become plausible.

Electronic entropy is usually treated as a secondary correction to structural stability, but under strong electronic excitation it can become a primary thermodynamic driving force. Here we show that electronic entropy can drive both polymorphic and stoichiometric phase transformations in compressed iron oxides. Using finite-temperature density functional theory, we calculate the electronic-temperature-dependent Gibbs free energies of Fe$_2$O, FeO, Fe$_4$O$_5$, Fe$_3$O$_4$, and multiple Fe$_2$O$_3$ polymorphs, including $α$-, $ι$-, $ζ$-, $η$-, and $θ$-Fe$_2$O$_3$, over the pressure range 60--260 GPa. At 60-140 GPa, electronic excitation mainly reorganizes the relative stability of Fe$_2$O$_3$ polymorphs, driving transitions from $ι$-Fe$_2$O$_3$ to $η$-Fe$_2$O$_3$. At 180 GPa, the free-energy landscape becomes strongly competitive as FeO is stabilized over an intermediate range of electronic temperature, while $η$-Fe$_2$O$_3$ becomes favourable at higher T. At 220-260 GPa, the lowest-free-energy phase at low T is the Fe-rich compound Fe$_2$O, but increasing electronic temperature stabilizes FeO. These results demonstrate that electronic entropy can control not only the relative stability of crystal structures at fixed composition, but also the competition between different iron-oxide stoichiometries. The predicted electronic-entropy-driven phase boundaries provide a route to nonthermal structural transformations in ultrafast and high-energy-density experiments.

In the context of a new approach towards quantum foundation, the Born rule is proved under a weak condition through several steps. The sole weak condition behind the Born rule is called the transition probability principle, which is closely related to the likelihood principle of statistics. This condition is discussed from several points of view. The whole approach leads to a simpler state concept than the traditional one in finite-dimensional quantum mechanics.

Many computational fluid dynamics (CFD) algorithms solve partial differential equations by discretization, resulting in large and sparse systems of linear equations. While iterative methods are widely used to solve these systems classically, most existing quantum linear system solvers target the solution through matrix inversion rather than approximating it using an iterative procedure. In this work, we develop a quantum implementation of the Jacobi method based on quantum singular value transformation (QSVT). By reformulating the Jacobi iteration as a polynomial transformation of a block-encoded operator, the algorithm requires only a constant ancilla overhead with respect to the number of iterations while maintaining a circuit depth that scales linearly with the iteration number. We demonstrate the algorithm for one- and two-dimensional Poisson problems, including the pressure Poisson equation arising in Chorin's projection method for the lid-driven cavity flow. The proposed algorithm provides a promising building block for future quantum implementations of multigrid methods and preconditioning techniques, bringing quantum algorithms closer to established CFD solution strategies.

In this work, we characterize the glassy character of the Bose-glass phase in a disordered Bose-Hubbard model using three complementary diagnostics: the finite-temperature spectral function, spatial inhomogeneity, and the inverse participation ratio. Spectral analysis, obtained from finite-temperature Green's function and random phase approximation, shows that disorder introduces localized low-energy states within the Mott gap, eventually closing the gap at sufficiently strong disorder. Spatial inhomogeneity, calculated using the Gutzwiller ansatz, increases sharply with disorder and then saturates at moderate disorder strengths. The inverse participation ratio has been calculated from the exact diagonalization of a small system, and it reveals enhanced localization with stronger disorder. Increasing temperature suppresses these disorder-induced features: the low-energy spectral weight diminishes, the spatial inhomogeneity varies more smoothly, and the IPR decreases. Taken together, these diagnostics show that disorder drives the development of glassy character, while thermal fluctuations gradually wash out its signatures. The early saturation of spatial inhomogeneity compared with the continued evolution of low-energy excitations and the inverse participation ratio demonstrates that no single diagnostic fully captures the evolution of the Bose-glass state, highlighting the need for a combined characterization.

Test oracles for quantum transpilers typically judge correctness by comparing compiled output against a reference: a statevector, a sampled distribution, or a unitary compared modulo global phase. A companion empirical study measures how often that choice fails. Roughly 28% of merged Qiskit transpiler bug-fixes (95% Wilson CI 19-40%) repair a fault that corrupts layout metadata, global phase, or run-to-run reproducibility while output stays correct: invisible to a black-box output-equivalence oracle by construction. This paper closes that gap with a fault-class-matched, layout-aware, width-tiered oracle family: a layout/permutation contract checker and a contract-level metamorphic relation (MR-1) for the metadata channel, a global-phase tracker for the phase channel, and a determinism runner for reproducibility. Verified from source on nine real, merged Qiskit transpiler regressions (three per channel), the output-equivalence oracle is blind throughout and the matched mechanism fires on every case. A 675-configuration sweep of the contract/metadata invariant finds no false positive. Synthetic mutant families confirm reliability at scale: 1.00 sensitivity and specificity across 36 mutants apiece for the contract/metadata and global-phase channels, and 1.00 sensitivity (95% CI 0.44-1.00) for reproducibility on the three circuits where the mutation is constructible. The contract checker costs two to six orders of magnitude less than a plain output check, the global-phase tracker is comparably cheap within its exact tier, and only the metamorphic relation carries a bounded cost. Ported natively to pytket/tket, the global-phase mechanism transfers cleanly, an identical 1.00/1.00 result with phases recovered to double-precision accuracy, evidence against a Qiskit-specific artifact.

Universal power-law decay of spin-mixing oscillations has been observed in a harmonically trapped spin-$3/2$ Fermi gas, whose exactly equally spaced spectrum represents a highly special case. To gain insight into the origin of this behavior, we investigate the dynamics in traps with increasing and decreasing level spacings, represented by the infinite square well and the Pöschl--Teller potential, respectively. Despite pronounced differences in their single-particle spectra, all systems exhibit power-law decay of coherent oscillations, described by $A(t) = A_{0} - γt^α$. The exponent $α$ remains insensitive to particle number, interaction strength, and the overall energy scale, but exhibits systematic differences among traps with distinct spectral structures. In contrast, the decay parameter $γ$ is strongly influenced by both the spectral structure and the overall energy scale. These findings demonstrate that power-law decay is not restricted to the harmonic trap but persists across qualitatively distinct spectral structures. The observed variation of $α$ among different traps further suggests that the underlying single-particle spectrum plays an important role in shaping the decay dynamics.

A generalisation of the Leggett-Garg inequality (LGI) and the Bell-CHSH inequality is proposed in this work, by replacing a classical probability notion with an extended probability notion. The extended probability serves as an underlying layer of reality to the classical probability. Within the consistent history framework, the underlying layer is so-called a non-settleable history. Hence, the bounds of the LGIs and Bell-CHSH inequalities are extended. The resulting generalised inequalities are satisfied without violation for arbitrary measurement settings. Furthermore, generalised Macro- realism and generalised Local realism are introduced and analysed within the extended probability framework without relying on an explicit measurement. This opens up further possibilities on one of the great pursuits in physics, understanding on how a quantum system can possess classical properties.

We obtain a complete characterization of eventually entanglement breaking (EEB) unital channels in terms of some simple commutation properties of their eigenvectors. Specifically, the following properties are equivalent for a unital channel: (i) it is EEB; (ii) it is eventually positive partial transpose (PPT); (iii) it is eventually mixed twisted dephasing; and (iv) its eigenvectors corresponding to non-zero eigenvalues commute with all its peripheral eigenvectors. Similar results hold for one-parameter semigroups of unital quantum channels, where continuity forces such semigroups to become primitive. We employ a matrix integral technique inspired by a result of Watrous. We also characterize the extreme points of the convex set of unital EB channels and, using this characterization and the theory of equiangular tight frames (ETFs), identify several extreme points beyond the twisted dephasing channels.

Identifying a low-entanglement eigenstate inside a many-body spectrum and preserving it during measurement are distinct tasks. We construct an explicit local ring Hamiltonian with an exact cluster-state eigenvector and study continuous monitoring of its stabilizer defects. For arbitrary mixed inputs, the conditional cluster fidelity is the initial target weight divided by the no-observed-click probability. A positive defect-operator gap gives finite-time bounds that hold for noncommuting Hamiltonian dynamics, nonnormal effective generators and imperfect detection. At fixed total monitoring rate, the guaranteed exponent falls inversely with system size; high conditional fidelity does not remove the preparation cost set by the initial overlap. Exact diagonalization up to eleven qubits gives finite-size evidence for a cluster-state outlier in a chaotic spectral background. Independent matrix and trajectory calculations verify the dynamics and a conservative coherent-error bound. This construction specializes established scar embedding and nondemolition verification frameworks, with explicit measurement assumptions, finite-time guarantees and resource limitations.

Characterizing the phonon distribution of trapped-ion motional states is essential for many applications in quantum information processing, but existing methods become ill-conditioned beyond the Lamb-Dicke regime. We overcome this limitation by recasting phonon-state reconstruction as a filter-function inversion problem. Using composite pulses on the carrier and multiple sidebands, we engineer well-conditioned filters in phonon space to characterize pure and mixed states, study heating dynamics, and reconstruct Fock states up to $n=250$.

An imperfect many-body revival does not by itself certify the entanglement of the returning state. We give a finite-record protocol for graph-edge localizable entanglement along scar wavepackets of a graph-dressed PXP chain. The target cluster state has nonzero energy variance, so neither an exact target eigenstate nor a dark-state embedding is assumed. Fresh binary probes of the undeformed Hamiltonians Pauli terms have a fully separable explanation, even within the dressed blockade sector. Adding local graph-stabilizer probes makes established entanglement witnesses accessible with simultaneous confidence bounds. For a specified square-root instrument, an imposed worst-case disturbance budget fixes the strength that minimizes the equal-allocation Hoeffding sufficient sampling cost. A local commutator bound accounts for finite-duration ancilla pulses while the Hamiltonian remains active. We test the protocol on chains through twenty spins, under perturbed dynamics, and with independent implementations. At the first twenty-spin return, synthetic weak records certify all nineteen graph edges. Generator, two-color, bounded-weight, and full-group benchmarks separate this localizable resource from genuine multipartite certification. The protocol measures recoverable entanglement in a known scar wavepacket, with explicit calibration and limits on its physical and statistical interpretation.