We present an exact spectral and dynamical analysis of continuous-time quantum walks on barbell graphs and two variants of star-of-cliques graphs, obtaining closed-form eigenvalues, eigenvectors, eigenstate inverse participation ratios (IPRs), and long-time dynamical IPRs ($\overline{\mathrm{IPR}}$) for all families and vertex types. The central finding is that localization in these graphs arises through three distinct mechanisms, each responsible for a different vertex class: null-coupling confinement, in which dark modes have exactly zero amplitude at the intersubgraph connection and are therefore confined within individual cliques for all $n$; destructive-interference standing waves, whose opposite phase on either side of a structural bottleneck suppresses amplitude flow across it; and invariant-subspace dynamical localization, in which a large degenerate eigenspace drives $\overline{\mathrm{IPR}}\to 1$ for walks initialized at clique interior vertices—a result we establish through exact, vertex-specific dynamical IPR, in contrast to the graph-averaged treatments of degeneracy-driven trapping in prior work. In the barbell, clique interior vertices achieve $\overline{\mathrm{IPR}}\to 1$ while bridge vertices saturate at $1/2$. In variant 1 of the star-of-cliques construction, where every clique vertex connects to the hub, both hub and clique vertices achieve $\overline{\mathrm{IPR}}\to 1$. Restricting each clique to a single bridge connection (variant 2) reduces the hub's $\overline{\mathrm{IPR}}$ from 1 to $1/4$—fixed by its participation in only three eigenmodes regardless of graph size—while bridge and clique vertices retain $\overline{\mathrm{IPR}}\to 1$. Each mechanism responds differently to structural perturbation: The null-coupling mechanism is exact; the interference mechanism relies on the reflection symmetry between the two sides of the bottleneck; and the invariant-subspace mechanism is asymptotic in graph size. These results provide analytically solvable examples of how spectral degeneracy and connectivity together determine long-time quantum transport in modular networks.

We develop a comprehensive quantum estimation framework to quantify how precisely gravitationally induced decoherence can be inferred in optomechanical systems, using single-mode Gaussian probe states. Our approach combines a microscopic description of the gravitational diffusion mechanism with quantum Fisher information to determine the ultimate sensitivity achievable in principle. We show that gravitational diffusion leaves distinct signatures in the mechanical state, both during transient evolution and in the stationary regime. Finally, we identify how probe state preparation shapes the attainable precision, thereby establishing fundamental limits for detecting and estimating gravity-driven decoherence.

Understanding the limitations imposed by noise on current and next-generation quantum devices is a crucial step toward demonstrating practical quantum advantage. In this work, we investigate the accumulation of entropy density as a benchmark to monitor the performance of quantum processing units (QPUs). We provide a proof-of-principle demonstration of our methodology which entails developing simple heuristic models of how entropy accumulates, testing them against real QPU data, and finally using these models to determine a circuit volume threshold above which quantum advantage is unattainable. Monitoring entropy density not only offers an alternative approach that complements existing circuit-level benchmarking techniques, but, more importantly, it bridges the gap between circuit-level and application-level benchmarking protocols. In particular, our heuristic model of entropy accumulation allows us to outperform existing techniques that bound the circuit-size threshold for quantum advantage.

We present a quantum-native framework for auxiliary-field quantum Monte Carlo (AFQMC), viewed as imaginary-time projection for ground-state calculation through an ensemble of one-body propagators driven by stochastic auxiliary fields. Starting from a Feynman-Kac representation, each trajectory is converted into a sequence of piecewise-constant one-body generators using stochastic Magnus expansions up to second order. The resulting nonunitary one-body slices are implemented either by unitary dilation with a small ancilla register or by an equivalent system-only linear-combination-of-unitaries (LCU) form. The dilation formulation gives a coherent fault-tolerant segmented projector algorithm with linear scale-over-gap dependence, while the LCU formulation gives a near-term sampled estimator whose circuits are fermionic Gaussian and avoid the explicit dilation register. The two modes have different resource assumptions and different manifestations of the AFQMC sign and phase problem: estimator variance in the sampled near-term mode and normalization or postselection-amplitude cost in the coherent mode. Benchmarks on the Hubbard model verify the dilation and stochastic Magnus errors classically, test segment chaining, and demonstrate proof-of-principle multistep executions on IBM quantum hardware.

We formulate a spatial extension of the Leggett-Garg inequality by considering three distant observers locally measuring a many-body system at three subsequent times. The spatial form is especially suitable to test the ability of quantum devices to generate spatiotemporal correlations in a Hamiltonian-agnostic manner. We illustrate our proposal for a Heisenberg chain in a magnetic field, showing indeed that the first inequality-violation time scales proportionally to the distance between measuring parties. We attribute this phenomenon to Lieb-Robinson physics and, confirming this connection, we find that violations are anticipated when increasing the interaction range. The inequality violation is readily observable in current quantum simulation platforms, particularly Rydberg atoms' arrays and ultracold atoms in optical lattices. In outlook, spatial Leggett-Garg inequalities constitute a practical tool for benchmarking the complex nonrelativistic dynamics of many-body quantum systems.

Micromotion in radio-frequency ion traps is generally considered detrimental for quantum logic gates and is typically minimized in state-of-the-art experiments. However, as a deterministic effect, it can be incorporated into quantum control frameworks aimed at designing high-fidelity quantum logic controls. In this work, we demonstrate that micromotion can be beneficial to the design of fast entangling gates utilizing the radial modes of a two-ion crystal, particularly in the subtrap-period regime where high-fidelity control sequences are identified with operation times ranging from hundreds of nanoseconds to microseconds. Through analysis of select fast gate solutions, we uncover the physical origin of micromotion enhancement and further study the induced gate error under experimental noise and control imperfections. This analysis establishes the feasibility of realizing high-fidelity entangling gates in hundreds of nanoseconds using the micromotion-sensitive radial modes of trapped-ion crystals.

We show numerically that a repulsive Bose-Einstein condensate can be driven into implosive dynamics by a direct topological quench. We first realize giant vortices by quasiadiabatic phase imprinting, and then perform a sudden anti-imprint that cancels the accumulated winding in a single step, abruptly switching the condensate from a highly charged vortex state to the trivial sector. The resulting phase-density mismatch launches a rapid inward radial flow and produces a strong central density buildup, despite the repulsive interactions. After the first implosion, the dynamics evolves into circular nonlinear wave fronts that subsequently undergo breaking of azimuthal symmetry (axisymmetry) down to a polygonal one, whose shape is determined by the way the giant vortex is built. These results establish topological engineering as an effective tool for studying implosive dynamics and symmetry-breaking instabilities in quantum fluids.

Efficient microwave-to-optical frequency conversion (MOC) using Rydberg atoms is promising for radiometry, electrometry, and hybrid quantum networks. However, in free space, the total system efficiency can be much lower than the internal atomic conversion efficiency because of the large mismatch between microwave wavelength, optical wavelength, and atomic-ensemble size. Here, we develop a systematic theoretical framework in which the total conversion efficiency is factorized into microwave mode-matching efficiency, optical spin-wave extraction efficiency, and internal coherent conversion efficiency. In the regime ${\lambda }_{\mathrm{m}}\gg L\gg {\lambda }_{\mathrm{o}}$, the atomic ensemble couples to the microwave field as a collective dipole, whereas its coupling to the optical field is governed by a phase-matched spin-wave mode. We show that the total efficiency is primarily limited by microwave mode matching. For an ideal diffraction-limited Gaussian microwave mode coupled to this collective dipole, the microwave extraction factor is bounded by about $3/16$ under standard polarization and orientation averaging. This analysis provides a transparent benchmark for evaluating free-space Rydberg MOC and identifies microwave mode matching as the key target for experimental optimization.

The operational resource theory (ORT) measure is a nonclassicality measure for bosonic states, notable for its resource-theoretic properties and connection to metrology. However, it can be difficult to evaluate, being linked to an optimization problem for mixed states. Here, we present ORT measure calculations for mixed states with photon-number coherence. We give exact formulas governing the ORT measure of a broad class of rank-two mixed states, and numerical solutions for some higher-rank states. We also compare the nonclassicality of these states to their metrological power, thus showing in what regimes the metrological power manages to saturate the ORT bound. Throughout, we consider the role of coherence. In particular, we show that nonclassicality and metrological power never increase under bosonic dephasing, but may plateau in a manner similar to entanglement sudden death. Nevertheless, lowering photon-number coherence more freely can sometimes yield more nonclassical and metrologically useful states.

In open quantum systems, reduced dynamics is commonly described by a master equation, whose Liouvillian gap closing (LGC) typically signals the emergence of decoherence-free subspace. By contrast, the dynamics of the full system-environment compound is governed by the underlying Hamiltonian spectrum, where bound states in the continuum (BICs) can protect long-lived quantum resources. Despite these parallel perspectives, the relation between LGC and BIC formation has remained largely unexplored. Here we bridge this gap in a paradigmatic giant-atom waveguide platform and show that the occurrence of LGC can act as an indicator for a BIC in the full Hamiltonian description in this specific model. By engineering the giant-atom geometry, we further demonstrate rich dynamical regimes, including Rabi oscillations, fractional decay, and complete exponential relaxation, depending on the number of supported BICs, which can be tuned from three to zero. Remarkably, when two BICs become frequency degenerate, the long-time dynamics approaches a steady state rather than exhibiting persistent oscillations. Our results indicate that there may exist a spectral-dynamical correlation between effective Markovian and full Hamiltonian descriptions and provide a route toward flexible control of open-system dynamics.

This study investigates the dynamics and phase of a nonreciprocal quantum multilevel spin system in Landau-Zener (LZ) transitions. Using Majorana's stellar representation, we analytically derive the solution for the LZ transition in a nonreciprocal quantum spin-$j$ model. Building on the results of the nonreciprocal two-level system, we construct and derive the expressions for the transition probabilities in multilevel systems, the evolution matrix for nonadiabatic evolution around exceptional points, and the Stokes phase generated by this process. Furthermore, taking a nonreciprocal quantum three-level model as an example, we confirm the validity of the analytically derived results for multilevel systems through numerical simulations, with particular emphasis on the differences and similarities between the non-Hermitian and Hermitian cases. Finally, the results show that for a nonreciprocal spin-$j$ system with an arbitrary number of levels, the nonadiabatic evolution matrix defined in the bare basis during the LZ transition can be obtained from the direct product of the two-level nonadiabatic evolution matrices and can be expressed in terms of a weighted Wigner $D$ matrix. Moreover, transitions between any two adjacent energy levels generate a Stokes phase of the same form as that in the two-level system, and the Stokes phase corresponds exactly to the two rotation angles in the $X\text{−}Y$ plane of the rotation operator. As a concrete application, we map the three-level nonreciprocal LZ model to the three-band Su-Schrieffer-Heeger (SSH) model under an electric field and further extend this correspondence to general multiband SSH models. Our work provides a systematic and intuitive framework for analyzing non-Hermitian multilevel spin LZ dynamics, offering insights into nonreciprocal control, geometric phases, and nonadiabatic transitions in parity-time-symmetric and broader non-Hermitian quantum systems.

We present the formal derivation of a set of hierarchical equations of motion (HEOM) to compute system and environmental correlation functions in terms of a nonstationary underlying dynamics in complex time. This corresponds to partitioning the global validity of the HEOM spectral ansatz into local versions valid within a more limited time span. The non-Markovian indivisibility of the dynamics is recovered by gluing these HEOM patches to allow the propagation of degrees of freedom, whose purpose is to model how past system-bath dynamics affects the future. We illustrate the formalism to exemplify the regular dynamical case and the imaginary-time evolution.

In quantum many-body dynamics, locally encoded information typically scrambles across the entire system, becoming inaccessible to local probes. The upper bound of accessible information of local probes can be characterized by the Holevo information via optimal measurement. In this work, we investigate the information dynamics of quantum scrambling utilizing local randomized probes, quantified by the averaged accessible information (AAI). We derive an analytical expression for the AAI under Haar-random measurements and demonstrate that it is a function of purity of local reduced density matrix. Operationally, we employ the classical shadow protocol, using only single-qubit randomized Pauli measurements, to efficiently extract the AAI across extended subsystems. Through numerical simulations across diverse many-body paradigms, we show that the AAI can reveal distinct scrambling behaviors, resolving phenomena that range from dynamical confinement and ballistic transport to persistent scar revivals and many-body localization. This work highlights a pragmatic paradigm shift, from relying on optimal measurements to utilizing randomized local probes, for the characterization of complex quantum information dynamics.

Building scalable quantum networks relies on the core device of quantum memory. Most quantum cryptography protocols utilize nonorthogonal state encoding, inevitably causing efficiency loss due to mismatch of base vectors. The orthogonal state encoding protocol, proposed by Goldenberg and Vaidman [Phys. Rev. Lett. 75, 1239 (1995)], can overcome such drawbacks by traveling the two localized wave packets of orthogonal state assisted with quantum memory. However, most existing quantum memories, limited by intrinsic storage mechanisms, cannot simultaneously meet several key indicators required for quantum communication, including high bandwidth, high efficiency, and high fidelity. Here, we developed an on-demand ultrahigh bandwidth quantum memory, reaching 95.2% storage efficiency while retaining 98.2% single-photon interference visibility. Furthermore, we experimentally integrate it with an orthogonal state encoding quantum cryptography system, demonstrating its potential to outperform the conventional BB84 quantum key distribution. This work represents an experimental implementation of an orthogonal state encoding quantum cryptography system based on quantum memory, and lays the foundation for the future realization of long-distance quantum networks.

We use a quantum formalism for the partition function of the classical $XY$ model to identify a resilience phase transition in the zero-syndrome postselected sector of a noisy toric-rotor code. To this end, we consider a logical state of toric-rotor code under phase-shift noise described by a von Mises probability distribution. We then show that the fidelity of the noisy state with respect to the initial logical state is proportional to the partition function of the $XY$ model such that a Kosterlitz-Thouless phase transition at a critical temperature $T_c$ corresponds to a resilience phase transition at a critical width ${\sigma }_c$. To characterize this transition, we map the spin stiffness of the $XY$ model to a topological order parameter $0\le \lambda \le 1$, which quantifies the intrinsic resilience of the code to decoherence within the zero-syndrome subspace. We show that the initial logical state exhibits partial resilience to noise for widths less than ${\sigma }_c\approx 0.89$, where $\lambda$ satisfies $0<\lambda <1$ and drops discontinuously to zero at ${\sigma }_c$. We further discuss the implications of our results for postselected quantum error correction in the toric-rotor code in higher dimensions. Our work shows that the quantum formalism for partition functions provides a mathematically rigorous framework for studying noisy continuous-variable quantum codes.

We present an extended-algebra (EA) control workflow for fixed-horizon, bounded-amplitude quantum control. The method optimizes a state-transfer trajectory in a polynomial EA, projects the optimized lifted trajectory to native physical controls using a budgeted dictionary of product-formula approximants, and then refines the resulting waveform on the original idealized physical model with gradient ascent pulse engineering (GRAPE). The sub-Riemannian gradient ascent pulse engineering (SR-GRAPE) method and the direct-GRAPE baseline use the same physical Hamiltonian, amplitude bounds, time horizon, discretization, and terminal physical optimizer; the difference is the initialization supplied to the final physical-space optimization. For Greenberger-Horne-Zeilinger (GHZ) preparation with Ising-coupled qubits and local $x\mathrm{and}y$ drives, SR-GRAPE changes which basin is reached. In the five-qubit state-growing benchmark, SR-GRAPE reaches $\mathcal{F}\ge 0.99$ in $25/25$ trials with mean fidelity 0.9917, whereas direct physical-space GRAPE from random feasible initialization remains near the $\mathcal{F}=0.5$ GHZ plateau in all 25 trials. Six-qubit state-growing also gives $25/25$ successes at $\mathcal{F}\ge 0.99$, while direct GRAPE remains at mean fidelity 0.4998 with $0/25$ successes. In a seven-qubit resource-extended setting with $u_{max}=3$, SR-GRAPE again reaches $\mathcal{F}\ge 0.99$ in $25/25$ seeds with mean fidelity 0.9901, whereas the corresponding direct-GRAPE baseline remains at mean fidelity 0.5000 with $0/25$ successes. For the GHZ task, $\mathcal{F}>0.5$ certifies genuine multipartite entanglement; the $\mathcal{F}=0.5$ plateau does not cross this witness threshold.

Inspired by the self-fulfilling prophecy (SFP) mechanism introduced by Uys et al. [H. Uys et al., Phys. Rev. A 97, 060102(R) (2018)], we develop an unsharp-measurement–feedback framework for multipartite entanglement generation and stabilization in open quantum systems. The method formulates a branchwise fixed-point construction for entangled target states, with the two-qubit Bell state serving as a minimal example and Greenberger-Horne-Zeilinger and W states as representative multipartite benchmarks. Intercycle decoherence is incorporated using Kraus-type and Lindblad-type dissipation models, which give consistent ensemble-averaged behavior. We further introduce an adjoint-channel-based adaptive correction that compensates noise-induced deviations and accelerates convergence. Numerical simulations quantify the effects of dissipation, measurement-feedback frequency, and measurement strength on the attainable fidelity and resource tradeoffs. The results extend SFP-style measurement-feedback control from state-preparation protocols to a dissipation-aware protocol-level framework for multipartite entanglement generation.

We propose a representative, globally admissible phenomenological spectral density of the bath for the non-Markovian Brownian motion of an optomechanical resonator, motivated by the near-resonance experimental observation of a non-Ohmic spectrum in [Nat. Commun. 6, 7606 (2015)]. To avoid divergences arising from a naive global extrapolation, we propose a globally admissible, phenomenological bath spectrum that extends the experimentally observed, near-resonance non-Ohmic behavior beyond the measurement window while ensuring finite-bath-induced renormalizations and quadrature fluctuations of the resonator. The corresponding model of the structured environment produces a nonlocal mechanical response whose analytic pole structure encodes the observed linewidth. The resulting dissipation kernel exhibits a power-law-modulated exponential decay with transient negativity, signaling memory effects. In the weak-coupling regime, the optical readout based on homodyne detection enables near-resonance spectroscopy and, with a calibrated drive on the resonator, permits, in principle, the reconstruction of the full mechanical susceptibility, thereby providing access to both the dissipative and dispersive bath contributions. Our results provide a consistent route from locally inferred spectral properties to globally admissible open-system descriptions and establish a framework for probing structured environments in cavity optomechanics.

Using supersonic expansion, we create a time-gated, directional beam of Xe atoms with a narrow momentum distribution and detect their collisions with a levitated nanosphere cooled to its quantum ground state. We observe individual momentum kicks below 50 $\mathrm{keV}/c$ with $96\%$ confidence and distinguish directional momentum transfer from the atomic beam against the background of thermal collisions. Our experiments constitute a first step toward the exploration of distance-dependent short-range interactions between atoms and levitated systems, as well as toward the use of levitated platforms for impulsive force sensing in previously unexplored parameter regimes.

The circulator is one of the crucial devices in quantum networks and quantum simulations. We propose a four-port single-photon circulator based on a waveguide quantum electrodynamics system, where a driven $\mathrm{\Lambda }$-type giant atom is coupled to two coupled-resonator waveguides. We find that the phase difference between the atom and the upper (lower) waveguide can control the crossover between reciprocal and nonreciprocal photon transmission in the respective waveguide. Here, the phase difference refers to the relative phase carried by these coupling constants. Under specific phase conditions, the system exhibits multiple circulation modes, including cross-type circulation as well as fully unidirectional clockwise or counterclockwise photon transport. Meanwhile, the frequency position of the photon circulation can be controlled by adjusting the external driving frequency. This discovery introduces a control dimension for designing reconfigurable quantum photonic devices.