Papers

We generalize the canonical Hopfield model of associative memory, which stores classical states of individual spins, to store entangled quantum states. The construction is based on truncated projector-sum Hamiltonian, and we explicitly consider a special case that stores dimer singlet coverings of a spin-1/2 system. We analyze the stability of the stored memories and find that the capacity – the number of stable patterns – scales faster with the system size than one would expect from a naive analogy with the standard Hopfield model, suggesting a possible quantum advantage.

We propose a scheme for mediating many simultaneous, fast entangling gates between pairs of polar molecules using Rydberg atoms. By using microwave drives, the dipolar interactions between Rydberg atoms are nullified. Using the freedom left in the microwave dressing parameters, the Rydberg van der Waals interactions are minimized and the Rydberg-molecule interaction is tuned into resonance, allowing for the mediation of a modified iSWAP gate between molecules. In the example of mediating gates between $\rm{{}^{23}Na {}^{133}Cs}$ molecules with $\rm {}^{133}Cs$ atoms, the gate is more than two orders of magnitude faster than an equivalent direct molecule-molecule gate. We model the decay of the dressed Rydberg states and the motion of the atom and molecules and obtain a leading-order estimate of the resulting gate infidelities. Finally, we show that by detecting the state of the Rydberg atom after a gate, a subset of gate errors can be converted into erasure errors and mitigated by post-selection or quantum error-correction.

Tin monosulfide (SnS) is a layered IV-VI semiconductor with strong in-plane anisotropy and promising properties for optoelectronic and ferroic applications. However, obtaining large, continuous, and morphologically well-defined SnS crystals remains challenging. Here, we report the growth of large-area SnS crystals using chemical vapor deposition with separate elemental Sn and S precursors. By controlling the precursor temperatures, source positions, substrate temperature, carrier-gas flow, and hydrogen flow, we obtain SnS crystals with lateral dimensions approaching 350 micrometers. The optimized growth occurs with the Sn source at approximately 750 degrees C, the S source at approximately 230 degrees C, and the substrate maintained near 650-680 degrees C, using Ar/H2 flow rates of 120/10 sccm. X-ray diffraction shows a dominant SnS (111) reflection with no detectable secondary crystalline tin-sulfide phase within the measurement sensitivity. Raman spectroscopy reveals six characteristic SnS phonon modes at approximately 39.3, 48.8, 95.2, 165.0, 193.1, and 219.1 cm^-1. In particular, the low-frequency modes near 39 and 49 cm^-1 are clearly resolved with FWHM values of approximately 2.52 and 2.37 cm^-1, respectively. SEM and AFM measurements further show large continuous crystals and a relatively smooth nanoscale surface. Growth on mica produces more regular square and rectangular flakes, with lateral dimensions approaching 300 x 300 micrometers, while crystals grown on SiO2/Si are more frequently fractured or irregular at their edges. These results demonstrate a practical growth window for obtaining large-area SnS crystals suitable for further optical, electrical, and device studies.

Closed paths of observable algebras can enact logical gates. We show that algebras of fixed block structure have a unique unitarily invariant parallel transport, recovering Berry–Wilczek–Zee transport on bands. On positive-dimensional configuration spaces, the holonomy group is the special-unitary part of the normalizer: every inner logical gate and every equal-type sector permutation is attainable. Given a compatible gapped Hamiltonian and access to the required paths, inner logical gates can be implemented adiabatically by isospectral control of a band refinement.

We report forward random-circuit sampling (RCS) on the 120-qubit Nighthawk r2 superconducting processor (ibm_phoenix) with square-lattice connectivity, using 61 qubits, native CZ gates, and the standard cloud execution stack with no benchmark-specific calibration. Two independent fidelity estimators—mirror benchmarking and three- and four-patch cross-entropy benchmarking (XEB)—agree with each other at every measured depth, the mirror from 4 to 40 cycles and the patched estimators from 20 to 40 cycles, across more than two orders of magnitude of fidelity decay, and exceed the first-generation Nighthawk r1 device by more than an order of magnitude at fixed depth. The 36-cycle circuits sit at the depth where tensor-network contraction cost saturates at system size: a contraction-cost estimator validated against the published Sycamore and Zuchongzhi networks places the single-amplitude cost at $\sim$$10^{22}$ complex operations. At $F_{\mathrm{XEB}}(36)=2.3\times10^{-3}$ under favorable memory assumptions this implies $1.2\times10^{27}$ machine operations within the bounded-fidelity rejection-sampling model — more than a century of runtime on the Frontier supercomputer — to collect a $10^{6}$-sample ensemble, which takes only 19\,s on Nighthawk r2. To our knowledge, this is the first demonstration of quantum advantage for a vanilla random-circuit sampling on a commercially and broadly accessible quantum processor that most non-expert quantum computer users can easily replicate.

We prove that the regularized, stabilized sandwiched Rényi divergence of finite-dimensional quantum channels converges to their regularized relative entropy as the Rényi order tends to one. The key tool is the channel hockey-stick divergence: Gour's Stinespring approximation bound and a Schatten norm estimate amplify an asymptotic bound below one into exponential decay at higher threshold rates. For channel pairs with finite max-relative entropy, known operational connections then give exponential strong converses for parallel and adaptive discrimination, a sharp zero–one testing law, and the subchannel asymptotic equipartition property.

We study non-stabilizerness (magic) in the ground state of $(2+1)$-dimensional $\mathrm{SU}(2)$ Hamiltonian lattice gauge theory with matter, formulated in the dressed-site basis in the hardcore-gluon truncation and restricted to the zero baryon-number sector. Using matrix product states, we compute three facets of magic: the second-order stabilizer Rényi entropy (SRE) $M_2$, its non-local component $M_2^{\rm NL}$, and a lower bound in terms of the anti-flatness $F$ of the entanglement spectrum. We also prove a stronger form of the sandwich relation: $-\log_2(1-4F)\le M_2^{\rm NL}\le M_2$; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, thus resolving the open problem of finding the maximal lower bound. We emphasize a structural distinction that makes the non-local quantities the physically preferred diagnostics: whereas the full SRE depends on the (non-unique) encoding of the gauge-invariant local Hilbert space into qubits, both the non-local magic and the anti-flatness are invariant under site-local re-encodings and are therefore intrinsic to the state and bipartition. By varying the gauge coupling on lattices up to $6\times 6$ with bond dimension up to $128$, we find that the non-local magic furnishes a sharper and more bond-dimension-friendly probe of the gauge-matter delocalization crossover compared to the full SRE or the gauge-invariant entanglement entropy, retaining a clear signal at bond dimensions well below those needed to converge the ground state itself.

One of the primary applications of quantum mechanics is leveraging coherence to make incredibly sensitive measurements. One way to push the boundary of this sensitivity even further is to initially prepare a system in an entangled state, though the fragility of these states limits their usefulness. In this work, we propose a new approach by which sensitivity comes during the preparation of an entangled state, rather than first preparing the state and then using it for sensing. An adiabatic state preparation process is then accelerated by universal counterdiabatic driving, which is more robust to uncertainty in microscopic parameters than standard shortcuts to adiabaticity. Using a toy Lipkin-Meshkov-Glick model, we show that this approach can also lead to sensitivity beyond the Standard Quantum Limit.

Universal statistical laws are a hallmark of quantum chaos, usually associated with the loss of spatial structure. Here we show, theoretically and experimentally, that universality emerges already at shallow depths in chaotic quantum circuits. We derive universal distributions of output-probability fluctuations and test them on a programmable superconducting processor. Two-dimensional lattices, open one-dimensional chains, and periodic rings exhibit distinct universality classes, retaining signatures of geometry and boundary topology before full random-matrix behavior emerges. Within each class, the distributions depend on only two parameters: an effective many-body Thouless length and the accumulated number of incoherent errors. Extracting these directly from measured bitstring frequencies provides access to scrambling, entanglement growth of the target state, and global fidelity, without reconstructing or classically simulating the implemented circuit. We also identify a noise-driven transition between output statistics retaining system-wide quantum correlations and those reproducible by independent small patches. Our results establish finite-depth universality as a practical tool for probing deep properties of quantum processors.

We find the shape of the modes containing most of the entanglement between two disjoint spherical regions in the vacuum of a free massless real scalar field in 1+3 Minkowski spacetime. Using the Klco-Beck-Savage method we approximate the field and momentum profile of the vacuum most entangled modes (MEMs) between two spheres. We define a non-perturbative mode-swap entanglement harvesting protocol where two spacelike separated probes extract the maximal amount of entanglement between two regions. Our results are a first step in the direction of understanding the local entanglement structure of quantum fields, pinpointing the exact degrees of freedom that encode accessible quantum correlations in QFT.

Determining a noisy quantum channel's classical capacity and entanglement cost generally requires regularization over many channel uses. We remove both regularizations for every qubit-to-qubit channel admitting a pure output. For each such channel, Holevo information, channel entanglement of formation, and parallel entanglement cost are additive with those of any finite-dimensional partner channel. This class includes all qubit-to-qubit channels of Kraus rank at most two. For the amplitude damping channel with damping probability $p$, the unassisted classical capacity equals the known single-use Holevo information, attained by a binary pure-state ensemble with collective decoding, and the entanglement cost is $h_2((1+\sqrt p)/2)$ ebits per use. The common mechanism is a support criterion for strong superadditivity of entanglement of formation: one marginal has no support on the sector in which both local systems are orthogonal to fixed distinguished vectors. We prove this criterion in arbitrary finite dimensions using a triangular block-matrix entropy inequality and decompositions preserving two expectations. For amplitude damping, we also derive an exact finite-block Holevo deficit, identify the unique optimal average input for $p<1$, and construct a binary Kraus representation attaining the uniform formation bound.

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 $\Omega(N^{1/2})$. 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 $\chi^2$-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 $2.6058$. The result also holds for non-Hermitian Hamiltonians that are Hermitian with respect to a fixed metric.

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 can allow multiple optical-control channels to scale without a proportional multiplication of independent frequency references. Our work establishes a 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, which can be implemented with most of the present rare-earth ions hosted in various types of solids. Using HAGEM, a quantum memory device with one billion temporal modes per second can be developed with current available technologies. To validate the memory protocol, we conducted some proof-of-concept experiments. 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 proposed memory protocol and material, we experimentally demonstrate a single-mode quantum optical storage efficiency of 14.9% and a memory bandwidth of 200MHz, which can easily be extended to a few GHz. In addition, a multi-mode storage of four temporal modes is achieved with a storage efficiency of 1.3%. Broadband & large-multimode quantum memory device with a long storage time enabled by HAGEM integrating with the current available entangled photon pair source and tunable delay lines, a quantum repeater network with an entanglement distribution rate on the order of 1kHz - 10kHz can be created with a communication distance around 100km. This will greatly facilitate the development of quantum networks in near future.

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 $\delta^3 \le C\varepsilon$ that explicitly relates the minimal one-site symmetry defect $\delta$ 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 $|\lambda|^{-3}$ in the perturbation strength $\lambda$. 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 $t=o(|\lambda|^{-3/2})$, 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 $\epsilon$, 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 $O(d^2\epsilon^{-1})$ copies, single-qubit measurements with only one qubit measured adaptively per copy, and $O(d^3)$ classical processing time per copy. The $\epsilon^{-1}$ 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 $O(d \epsilon^{-1})$ 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.