Quantum secret sharing (QSS) has emerged as a promising avenue for storing secret with quantum-enhanced security. However, practical applications are hindered by the challenge for simultaneously implementing high-efficiency, high-security, and high-flexibility QSS with multiple users. Here we present an efficient, secure, and flexible QSS involving eight users with a continuous-variable eight-partite bound entanglement (BE) state, where only two nondegenerated optical parameter amplifiers are required. Such abilities are attributed to the generation of the eight-partite BE state with precise phase controlling systems and a large entanglement network, and fiber distribution with polarization-division multiplexing. In the QSS, a higher key rate can be demonstrated, when a secret is extracted through flexible combinations of more collaborative users. Our system may pave the way for the spatially separated multiuser quantum communications, while minimizing quantum hardware.

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error $\varepsilon$, provided that a sample set (of size $N$) of the states can be efficiently prepared and measured. In a recent work [Huang et al., Science 377, eabk3333 (2022)], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, $N=m^{\mathcal{O}\left(\frac{1}{\varepsilon }\right)}$, was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension $m$ is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the uniform prediction error $\varepsilon$ and the number of qubits, $n$, with $N=\mathrm{poly}({\varepsilon }^{-1},n,ln\frac{1}{\delta })$, where $\mathrm{poly}$ denotes a polynomial function, and ($1-\delta$) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to $N=\mathrm{poly}({\varepsilon }^{-1},ln\frac{n}{\delta })$. Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase.

Reconstructing the state of quantum many-body systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present an efficient quantum tomography protocol that combines the state-factored with eigenvalue mapping to address the rank-deficient issue and incorporates a momentum-accelerated gradient descent algorithm to speed up the optimization process. We implement extensive numerical experiments to demonstrate that our factored gradient descent algorithm efficiently mitigates the rank-deficient problem and admits orders of magnitude better tomography accuracy and faster convergence. We also find that our method can accomplish the full-state tomography of random 11-qubit mixed states within one minute.

Quantum variational algorithms (VQAs) are highly promising to realize quantum advantages on near-term quantum devices. Existing VQAs based on a manually fixed quantum Ansatz are computationally inefficient due to noise and the limited coupling maps of these devices. Previous work considers various quantum architecture search (QAS) algorithms to autodesign a quantum Ansatz based on specific questions to improve the performance of VQAs. Compared to manual design, autodesign can more efficiently explore the large space of a possible Ansatz and achieve better performance. However, two main challenges in utilizing QAS to design quantum circuits efficiently are the tremendous amount of space required for candidate quantum circuits, and the disconnection between quantum devices and autodesign in terms of qubit mapping and quantum noise. To address these issues, we propose an adaptive diversity-based quantum Ansatz search algorithm to efficiently generate the optimal quantum circuit based on device qubit mapping and noise. By considering the diversity among different candidate circuits and adaptively adding circuit depths, our approach only needs to focus on a small optimization space at each iteration step. In addition, the synchronization of optimizing circuit structure and aligning qubit mapping enables us to generate quantum circuits while avoiding additional mapping overhead. We evaluate the performance of our algorithm on simulators and real quantum devices for quantum eigenvalue problems and classification tasks. Results demonstrate that quantum circuits generated by our method outperform both a fixed hardware-efficient Ansatz and randomly generated quantum circuits in terms of final performance and resource-saving. Our algorithm provides a flexible way to efficiently generate excellent quantum circuits for significantly improving the performances of VQAs on near-term quantum devices.

The mixed state transport properties of type-II superconductors are strongly influenced by the dynamic behavior of quantized magnetic fluxoids around the critical temperature ($T_c$), where a combination of normal and superconducting properties is exhibited. To understand the mixed state transport properties of type-II superconducting NbN ultrathin films (2D) we measured sheet resistance ($R_{xx}^M$) and Hall resistance ($R_{xy}^M$) of a 5-nm-thick NbN film around $T_c$ (10.75 K) at temperatures 10.40, 10.68, and 10.77 K. Hall resistance (HR) was measured in external out-of-plane and in-plane magnetic fields up to 6 T, using 100 $\mu \mathrm{A}$ and 1 mA driving current in Van der Pauw geometry. The electric field of applied bias and Lorentz force of applied external magnetic field causes a movement of the normal conducting electrons within each fluxoid. The moving fluxoids cause dissipation and generation of Hall voltage. We developed a macroscopic analysis of the Hall resistance arising from fluxoids, to advance the differentiation between dissipating current and superconducting currents in type-II superconductors at $T_c$. We have extracted the number of normal conducting carriers per fluxoid and areal density and mobility of the fluxoids in dependence on the external magnetic field. This differentiation provides valuable insights into the dissipation mechanisms observed during transport measurements, e.g., after localized heating due to single photon absorption in nanostructured type-II superconductors. Furthermore, the developed macroscopic analysis of Hall resistance of fluxoids shows promising potential for investigating the fundamental aspects of fluxoid-defect interactions in type-II superconductors.

Based on the recent experiments on the triangular lattice antiferromagnet ${\mathrm{Na}}_2\mathrm{BaCo}{\left({\mathrm{PO}}_4\right)}_2$, we propose the easy-axis XXZ spin-1/2 model on the triangular lattice, that exhibits a quantum spin supersolid, to be a precursory Dirac spin liquid. Despite the presence of a three-sublattice magnetic order as a spin supersolid, we suggest that this system is close to a Dirac spin liquid by exploring its spectroscopic response. The physical consequence is examined from the spectroscopic response, and we establish the continuous spectra near the $M$ point in addition to the $K$ point excitation from the spinon continuum on top of the three-sublattice order. Moreover, the satellite peaks were predicted at the mid-points connecting the $\mathrm{\Gamma }$ and $K$ points. This proposal offers a plausible understanding of the recent inelastic neutron scattering measurement in ${\mathrm{Na}}_2\mathrm{BaCo}{\left({\mathrm{PO}}_4\right)}_2$ and could inspire further research in relevant models and materials, such as ${\mathrm{K}}_2\mathrm{Co}{\left({\mathrm{SeO}}_3\right)}_2$ and ${\mathrm{Rb}}_2\mathrm{Co}{\left({\mathrm{SeO}}_3\right)}_2$, and even more anisotropic magnets like ${\mathrm{PrMgAl}}_{11}{\mathrm{O}}_{19}$.

The asymmetric simple exclusion process (ASEP) is a paradigmatic nonequilibrium many-body system that describes the asymmetric random walk of particles with exclusion interactions in a lattice. Although the ASEP is recognized as an exactly solvable model, most of the exact results obtained so far are limited to one-dimensional systems. Here, we construct the exact steady states of the ASEP with closed and periodic boundary conditions in arbitrary dimensions. This is achieved through the concept of transition decomposition, which enables the treatment of the multidimensional ASEP as a composite of the one-dimensional ASEPs.

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings.

A two-dimensional axisymmetric fluid model is used to simulate the dynamics behavior of an atmospheric-pressure helium plasma jet in the presence of a parallel magnetic field. The plasma jet is generated in a coaxial dielectric barrier discharge (DBD) driven by pulsed direct-current voltage. Comparative analysis of the plasma jet with and without the parallel magnetic field indicates that a slightly thinner plasma sheath inside the tube is present with the parallel magnetic field as a result of the decreased accumulated electrons on the inner surface of dielectric tube. After the streamer propagates outside the tube, a little more concentrated electron distribution in the annular wall is observed by applying the magnetic field because of the reduced electron diffusion in the radial direction and the confinement effect of the magnetic field on the electrons in the avalanche heads. The tiny reduction in the length of plasma jet is attributed to the $\mathit{E}$ × $\mathit{B}$ drift of charged particles. These results demonstrate that the parallel magnetic field has no apparent effect on the propagation of the plasma jet, and it contributes little to the performance improvement of the coaxial DBD, which agrees well with the previous experimental observations. This little impact of the parallel magnetic field on the coaxial DBD plasma jet may result from negligible contribution of the memory effect to the sole discharge pulse as well as the weak confinement effect of the applied magnetic field on the surface electrons that moves along the magnetic field lines under electrostatic repulsion.

We have investigated the magnetic ground state properties of the quantum spin trimer compound strontium hydroxy copper chloride $\mathrm{SrCu}{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$ using bulk magnetization, specific heat measurements, nuclear magnetic resonance (NMR), and electron spin resonance (ESR) spectroscopy. $\mathrm{SrCu}{\left(\mathrm{OH}\right)}_3\mathrm{Cl}$ consists of layers with isolated ${\mathrm{Cu}}^{2+}$ triangles and hence provides an opportunity to understand the magnetic ground state of an isolated system of $S$ = 1/2 arranged on an equilateral triangle. Although magnetization measurements do not exhibit a phase transition to a long-range ordered state down to $T$ = 2 K, they reveal the characteristic behavior of isolated trimers with an exchange of $J=154$ K. The Curie-Weiss behavior changes around 50–80 K, as is also seen in the NMR spin-lattice relaxation rate. In zero magnetic field, our specific heat data establish a second-order phase transition to an antiferromagnetic ground state below $T$= 1.2 K. We have drawn a magnetic field-temperature ($H\text{−}T$) phase diagram based on the specific heat measurements. The ESR data show divergence of the linewidth at lower temperatures, which precedes the phase transition to an antiferromagnetic long-range ordered state with unconventional critical exponents. The temperature variation of the $g$-factor further confirms the antiferromagnetic phase transition and reflects the underlying magnetocrystalline anisotropy of the compound.

Ionic liquids (ILs) are appealing electrolytes for their favorable physicochemical properties. However, despite their longstanding use, understanding the capacitive behavior of ILs remains challenging. This is largely due to the formation of a nonconventional electric double layer (EDL) at the electrode-electrolyte interface. This study shows that the short-range Yukawa interactions, representing the large anisotropically charged ILs, demix IL to create a spontaneous surface charge separation, which is reinforced by the strongly coupled charge interaction. The properties of the condensed layer, the onset of charge separation, and the rise of overscreening and crowding critically depend on the asymmetry of Yukawa interactions.

Open systems with balanced gain and loss, described by parity-time ($\mathcal{PT}$-symmetric) Hamiltonians have been deeply explored over the past decade. Most explorations are limited to finite discrete models (in real or reciprocal spaces) or continuum problems in one dimension. As a result, these models do not leverage the complexity and variability of two-dimensional continuum problems on a compact support. Here, we investigate eigenvalues of the Schrödinger equation on a disk with zero boundary condition, in the presence of constant, $\mathcal{PT}$-symmetric, gain-loss potential that is confined to two mirror-symmetric disks. We find a rich variety of exceptional points, re-entrant $\mathcal{PT}$-symmetric phases, and a nonmonotonic dependence of the $\mathcal{PT}$-symmetry breaking threshold on the system parameters. By comparing results of two model variations, we show that this simple model of a multicore fiber supports propagating modes in the presence of gain and loss.

Blebs, spherical membrane bulges of the cell membrane, are ubiquitous structures observed in various biological phenomena, including apoptosis, cell division, to bleb-based cell migration. The mechanics of blebbing have been characterized in terms of the actin cytoskeleton beneath the cell membrane. However, how changes in cortical mechanics relate to changes in the physical behaviors of the cell remains unclear. Here, we reconstitute a minimal model of the actomyosin cortex within liposomes. Upon laser ablation of the cortex, myosin-induced mechanical stresses are relaxed by different mechanisms—either cortical flows or membrane blebbing. For cortical flows, the cortex-membrane composite behaves as a viscoelastic fluid. By contrast, for ablation-induced blebbing, elastic stresses are accumulated, and the cortex behaves as a solid with a stress yield. These results highlight pivotal roles for membrane elasticity, cytoskeleton, and pressure in the mechanical responses of the actomyosin cortex.

The quantum Rabi model describes the coupling of a two-state system to a bosonic field mode. Recent theoretical work has pointed out that a generalized periodic version of this model, which maps onto Hamiltonians applicable in superconducting qubit settings, can be quantum simulated with cold trapped atoms. Here, we experimentally demonstrate atomic dynamics predicted by the periodic quantum Rabi model far in the deep strong-coupling regime. The two-state system is represented by two Bloch bands of cold atoms in an optical lattice, and the bosonic mode by oscillations in a superimposed optical dipole trap potential. The observed dynamics beyond the usual quantum Rabi physics becomes relevant when the edge of the Brillouin zone is reached, and evidence for collapse and revival of the initial state is revealed at extreme coupling conditions.

A superconductor (SC) in proximity to a ferromagnetic insulator (FMI) is predicted to exhibit mixed singlet and triplet correlations. The magnetic proximity effect of FMI spin splits the energy of Bogoliubov excitations and leads to a spin polarization at the surface for superconducting films that are thinner than the superconducting coherence length. In this work, we study manifestations of these phenomena in the properties of a magnetic impurity coupled via Kondo coupling to this FMI/SC system. Using the numerical renormalization group (NRG) method, we compute the properties of the ground state and low-lying excited states of a model that incorporates the Kondo interaction and a Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interaction with the surface spin polarization. Our main finding is an energy splitting of the lowest even fermion-parity states caused by the proximity to the FMI. As the Kondo coupling increases, the splitting grows and saturates to a universal value equal to twice the exchange field of the FMI. We introduce a two-site model that can be solved analytically and provides a qualitative understanding of this and other NRG results. In addition, using perturbation theory, we demonstrate that the mechanism behind the splitting involves the RKKY field and the triplet correlations of the spin-split superconductor. A scaling analysis combined with NRG shows that the splitting can be written as a single-parameter scaling function of the ratio of the Kondo temperature and the superconducting gap, which is also numerically obtained.

We study the computational complexity of simulating the time-dependent expectation value of a local operator in a one-dimensional quantum system by using temporal matrix product states(MPSs) and argue that it is intimately related to that of encoding temporal transition matrices and their partial traces. We show that we can upper-bound the rank of these reduced transition matrices by one of the Heisenberg evolution of local operators, thus making aconnection between two apparently different quantities, the temporal entanglement and the local operator entanglement(OE). As a result, whenever the local OE grows slower than linearly in time, we show that computing time-dependent expectation values of local operators using temporal MPSs is likely advantageous with respect to computing the same quantities using standard MPS techniques.

Nonlinearity-induced nonreciprocity is studied in a system comprising two resonators coupled to a one-dimensional waveguide when the linear system does not exhibit nonreciprocity. The analysis is based on the Hamiltonian of the coupled system and includes the dissipative coupling between the waveguide and resonators, along with the input-output relations. We consider a large number of scenarios which can lead to nonreciprocity. We pay special attention to the case when the linear system does not exhibit nonreciprocal behavior. In this case, we show how very significant nonreciprocal behavior can result from Kerr nonlinearities. We find that the bistability of the nonlinear system can aid in achieving large nonreciprocity. Additionally, we bring out nonreciprocity in the excitation of each resonator, which can be monitored independently. Our results highlight the profound influence of nonlinearity on nonreciprocal behavior, offering an avenue for controlling light propagation in integrated photonic circuits. Nonlinearity-induced nonreciprocity would lead to significant nonreciprocity in quantum fluctuations when our system is treated quantum mechanically.

We propose Hamiltonian quantum generative adversarial networks (HQuGANs) to learn to generate unknown input quantum states using two competing quantum optimal controls. The game-theoretic framework of the algorithm is inspired by the success of classical generative adversarial networks in learning high-dimensional distributions. The quantum optimal control approach not only makes the algorithm naturally adaptable to the experimental constraints of near-term hardware, but also offers a more natural characterization of overparameterization compared to the circuit model. We numerically demonstrate the capabilities of the proposed framework to learn various highly entangled many-body quantum states, using simple two-body Hamiltonians and under experimentally relevant constraints such as low-bandwidth controls. We analyze the computational cost of implementing HQuGANs on quantum computers and show how the framework can be extended to learn quantum dynamics. Furthermore, we introduce a cost function that circumvents the problem of mode collapse that prevents convergence of HQuGANs and demonstrate how to accelerate the convergence of them when generating a pure state.

We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the $\pi$-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background $\pi$-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal $d$-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by $(2+1)$-dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional $d$-wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases.