The 100 most-cited articles in Physical Review A, 2020

A machine learning design is developed to train a quantum circuit specialized in solving a classification problem. In addition to discussing the training method and effect of noise, it is shown that the circuits perform reasonably well on classical benchmarks.

Data representation is crucial for the success of machine-learning models. In the context of quantum machine learning with near-term quantum computers, equally important considerations of how to efficiently input (encode) data and effectively deal with noise arise. In this paper, we study data encodings for binary quantum classification and investigate their properties both with and without noise. For the common classifier we consider, we show that encodings determine the classes of learnable decision boundaries as well as the set of points which retain the same classification in the presence of noise. After defining the notion of a robust data encoding, we prove several results on robustness for different channels, discuss the existence of robust encodings, and prove a lower bound on the number of robust points in terms of fidelities between noisy and noiseless states. Numerical results for several example implementations are provided to reinforce our findings.

We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities efficiently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schr\"odinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more efficient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device.

We show that a class of vector vortex beams possesses a topological property that derives both from the spatially varying amplitude of the field and its varying polarization. This property arises as a consequence of the inherent skyrmionic nature of such beams and is quantified by the associated skyrmion number. We illustrate this idea for some of the simplest vector beams and discuss the physical significance of the skyrmion number in this context.

Effective Hamiltonian methods are utilized to model the two-qubit cross-resonance gate for both the ideal two-qubit case and when higher levels are included. Analytic expressions are obtained in the qubit case and the higher-level model is solved both perturbatively and numerically, with the solutions agreeing well in the weak-drive limit. The methods are applied to parameters from recent experiments and, accounting for classical cross-talk effects, results in good agreement between theory and experimental results.

The quantum alternating operator ansatz (QAOA) is a promising gate-model metaheuristic for combinatorial optimization. Applying the algorithm to problems with constraints presents an implementation challenge for near-term quantum resources. This paper explores strategies for enforcing hard constraints by using $XY$ Hamiltonians as mixing operators (mixers). Despite the complexity of simulating the $XY$ model, we demonstrate that, for an integer variable admitting $\ensuremath{\kappa}$ discrete values represented through one-hot encoding, certain classes of the mixer Hamiltonian can be implemented without Trotter error in depth $O(\ensuremath{\kappa})$. We also specify general strategies for implementing QAOA circuits on all-to-all connected hardware graphs and linearly connected hardware graphs inspired by fermionic simulation techniques. Performance is validated on graph-coloring problems that are known to be challenging for a given classical algorithm. The general strategy of using $XY$ mixers is borne out numerically, demonstrating a significant improvement over the general $X$…

This paper points out the importance of the assumption of locality of physical interactions, and the concomitant necessity of propagation of an entity (in this case, off-shell quanta---virtual gravitons) between two nonrelativistic test masses in unveiling the quantum nature of linearized gravity through a laboratory experiment. At the outset, we will argue that observing the quantum nature of a system is not limited to evidencing $O\left(\ensuremath{\hbar}\right)$ corrections to a classical theory: it instead hinges upon verifying tasks that a classical system cannot accomplish. We explain the background concepts needed from quantum field theory and quantum information theory to fully appreciate the previously proposed table-top experiments, namely forces arising through the exchange of virtual (off-shell) quanta, as well as local operations and classical communication (LOCC) and entanglement witnesses. We clarify the key assumption inherent in our evidencing experiment, namely the locality of physical interactions, which is a generic feature of interacting systems of quantum…

Quantum machine learning and optimization are exciting new areas that have been brought forward by the breakthrough quantum algorithm of Harrow, Hassidim, and Lloyd for solving systems of linear equations. The utility of classical linear system solvers extends beyond linear algebra as they can be leveraged to solve optimization problems using iterative methods like gradient descent. In this work, we provide a quantum method for performing gradient descent when the gradient is an affine function. Performing $\ensuremath{\tau}$ steps of the gradient descent requires time $O(\ensuremath{\tau}{C}_{S})$ for weighted least-squares problems, where ${C}_{S}$ is the cost of performing one step of the gradient descent quantumly, which at times can be considerably smaller than the classical cost. We illustrate our method by providing two applications: first, for solving positive semidefinite linear systems, and, second, for performing stochastic gradient descent for the weighted least-squares problem with reduced quantum memory requirements. We also provide a quantum linear system solver in…

Exceptional points (EPs) are degeneracies of classical and quantum open systems, which are studied in many areas of physics including optics, optoelectronics, plasmonics, and condensed matter physics. In the semiclassical regime, open systems can be described by phenomenological effective non-Hermitian Hamiltonians (NHHs) capturing the effects of gain and loss in terms of imaginary fields. The EPs that characterize the spectra of such Hamiltonians (HEPs) describe the time evolution of a system without quantum jumps. It is well known that a full quantum treatment describing more generic dynamics must crucially take into account such quantum jumps. In a recent paper [F. Minganti et al., Phys. Rev. A 100, 062131 (2019)], we generalized the notion of EPs to the spectra of Liouvillian superoperators governing open system dynamics described by Lindblad master equations. Intriguingly, we found that in situations where a classical-to-quantum correspondence exists, the two types of dynamics can yield different EPs. In a recent experimental work [M. Naghiloo et al., Nat. Phys. 15, 1232…

The performance of the circuit-based surface-GKP bosonic quantum error correction code under noise due to finite squeezing of the GKP states and photon losses is investigated. The authors show under what conditions fault-tolerant quantum error correction is possible with the surface-GKP code.

We present a method for reducing the number of non-Clifford quantum gates, in particularly T-gates, in a circuit, an important task for efficiently implementing fault-tolerant quantum computations. This method matches or beats previous approaches to ancillae-free T-count reduction on the majority of our benchmark circuits, in some cases yielding up to 50% improvement. Our method begins by representing the quantum circuit as a ZX-diagram, a tensor networklike structure that can be transformed and simplified according to the rules of the ZX-calculus. We then extend a recent simplification strategy with a different ingredient, phase gadgetization, which we use to propagate non-Clifford phases through a ZX-diagram to find nonlocal cancellations. Our procedure extends unmodified to arbitrary phase angles and to parameter elimination for variational circuits. Finally, our optimization is self-checking, in the sense that the simplification strategy we propose is powerful enough to independently validate equality of the input circuit and the optimized output circuit. We have implemented the…

An apparatus that uses optically levitated objects, together with active feedback cooling, is used to provide an order-of-magnitude improvement on the sensitivity of state-of-the-art accelerometers. The results pave the way to using such sensors as a part of large-scale particle detectors, for assessing the neutrality of matter and dark matter, and for studying short-ranged Yukawa forces.

Encoding a qubit in the continuous degrees of freedom of an oscillator is a promising path to error-corrected quantum computation. One advantageous way to achieve this is through Gottesman-Kitaev-Preskill (GKP) grid states, whose symmetries allow for the correction of any small continuous error on the oscillator. Unfortunately, ideal grid states have infinite energy, so it is important to find finite-energy approximations that are realistic, practical, and useful for applications. In the first half of this work we investigate the impact of imperfect GKP states on computational circuits independently of the physical architecture. To this end, we analyze the behavior of the physical and logical content of normalizable GKP states through several figures of merit, employing a recently developed modular subsystem decomposition. By tracking the errors that enter into the computational circuit due to imperfections in the GKP states, we are able to gauge the utility of these states for noisy intermediate-scale quantum devices. In the second half, we focus on a state preparation approach in…

The simultaneous ground-state cooling of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity-field mode has become an outstanding challenge in cavity optomechanics. This is because the dark modes formed by these mechanical modes decouple from the cavity mode and prevent extracting energy from the dark modes through the cooling channel of the cavity mode. Here we propose a universal and reliable dark-mode-breaking method to realize the simultaneous ground-state cooling of two degenerate or nondegenerate mechanical modes by introducing a phase-dependent phonon-exchange interaction, which is used to form a loop-coupled configuration. We find an asymmetrical cooling performance for the two mechanical modes and expound this phenomenon based on the nonreciprocal energy transfer mechanism, which leads to the directional flow of phonons between the two mechanical modes. We also generalize this method to cool multiple mechanical modes. The physical mechanism in this cooling scheme has general validity and this method can be extended to break other dark-mode and…

In this paper, we investigate the single-photon scattering and bound states in a one-dimensional coupled-resonator waveguide which couples to a single artificial giant atom with two or more coupling points. When the atom couples to the waveguide via two resonators, the single-photon reflection rate is characterized by either Breit-Wigner or Fano lineshapes. When the atom couples to the waveguide via multiple resonators, we show numerically how the destructive interference effect leads to a complete single-photon reflection. We also find a phase-transition phenomena for the multiresonator coupling case, which reveals that the upper bound state only exists when the atom-waveguide coupling strength is above a critical value.

Quantum-gate errors are a significant challenge for achieving precision measurements on noisy intermediate-scale quantum (NISQ) computers. This paper focuses on zero-noise extrapolation (ZNE), a technique that can be implemented on existing hardware, studying it in detail and proposing modifications to existing approaches. In particular, we consider identity insertion methods for amplifying noise because they are hardware agnostic. We build a mathematical formalism for studying existing ZNE techniques and show how higher order polynomial extrapolations can be used to systematically reduce depolarizing errors. Furthermore, we introduce a method for amplifying noise that uses far fewer gates than traditional methods. This approach is compared with existing methods for simulated quantum circuits. Comparable or smaller errors are possible with fewer gates, which illustrates the potential for empowering an entirely new class of moderate-depth circuits on near term hardware.

Considering the ground state of a quantum spin model as the initial state of the quantum battery, we show that both ordered and disordered interaction strengths play a crucial role in increasing the extraction of power from it. In particular, we demonstrate that exchange interactions in the $xy$ plane and in the $z$ direction, leading to the $XYZ$ spin chain, along with the local charging field in the $x$ direction substantially enhance the efficiency of the battery compared to the model without interactions. Moreover, such an advantage in power obtained due to interactions is almost independent of the system size. We find that the behavior of the power, although measured during dynamics, can faithfully mimic the equilibrium quantum phase transitions present in the model. We observe that with the proper tuning of system parameters, an initial state prepared at finite temperature can generate higher power in the battery than that obtained with zero temperature. Finally, we report that defects or impurities, instead of reducing the performance, can create a larger amount of quenched…

In this paper, we show that nonreciprocal unconventional photon blockade can be observed in a spinning cavity immersed in a degenerate optical parametric amplifier (OPA) driven by the laser driving with weak Kerr nonlinearities through the Fizeau drag. We analytically derive the optimal conditions for strong antibunching, which are in good agreement with those obtained by numerical simulations. Under the weak driving condition, we discuss the physical origins of the nonreciprocal unconventional photon blockade, which originates from the destructive interference between different paths from the ground state to two-photon states by driving the device from the left side. While the quantum interference paths are broken when the device is driven from the right side, which leads to the occurring of the photon bunching. Moreover, we extend the above results to the general non-Markovian regimes, in which the cavity couples with a thermal reservoir consisting of collection of infinite oscillators (bosonic photonic modes). We show nonreciprocal unconventional photon blockade exhibits a…

An 18-qubit GHZ state with multipartite entanglement is prepared and measured on a 20-qubit device. The detection technique used, which is based on measuring multiple quantum coherences, is robust to noise and only requires measuring the population in the ground state.

The excitation spectrum of a one-dimensional two-component bosonic mixture of ultracold atoms is studied by an extension of the Gross-Pitaevskii equation approach. The results can help distinguish the self-bound droplet state from the bright soliton.

The matrix product state (MPS) belongs to the most important models in, for example, quantum information sciences and condensed-matter physics. However, realizing an $N$-qubit MPS with large $N$ and large entanglement on a quantum platform is extremely challenging, since it requires high-level qudits or $n$-qubit gates with $n\ensuremath{\gg}2$ to carry or produce the entanglement. In this work, an efficient method that accurately encodes a given MPS into a quantum circuit with only one- and two-qubit gates is proposed. Essentially different from the existing compiling methods, our idea is to construct the unitary matrix product operators that optimally disentangle the MPS to a product state. These matrix product operators form the quantum circuit that evolves a product state to the targeted MPS with a high fidelity. Our benchmark on the ground-state MPSs of the strongly correlated spin models show that the constructed quantum circuits can simulate the MPSs with much fewer qubits than the sizes of the MPSs themselves. This method paves a feasible and efficient path to realizing…

We study the generation of a magnon blockade in a single-crystalline yttrium-iron-garnet (YIG) sphere coupled to a three-dimensional superconducting microwave resonator that interacts with a superconducting qubit. Based on the indirect coupling between the Kittel mode of YIG and the superconducting qubit mediated by the virtual photon excitation in the microwave cavity, we propose two different mechanisms for observing the magnon blockade effect in the ferromagnetic sphere. The first one is to use the strong anharmonicity of the dressed states of the coupled qubit-magnon system. However, the strong magnon antibunching can only be achieved under the strong-coupling regime. To relax this constraint, we propose another quantum interference method to produce and enhance the magnon blockade effect with the moderate-coupling strength. By optimizing the relative phase and the strength ratio of the external driving fields applied to the YIG and qubit, we show that the much stronger magnon antibunching with significantly increased steady-state mean magnon numbers can be realized by the…

We present a comprehensive theoretical study of the cross-resonance gate operation covering estimates for gate parameters and gate error as well as analyzing spectator qubits and multiqubit frequency collisions. Starting from the Josephson nonlinearity and by accounting for the eigenstates renormalization, due to counterrotating terms, we derive a starting model for the cross-resonance gate with modified qubit-qubit interaction and drive matrix elements. Employing time-dependent Schrieffer-Wolff perturbation theory, we derive an effective Hamiltonian for the cross-resonance gate with estimates for the gate parameters calculated up to the fourth order in drive amplitude. The model with renormalized eigenstates lead to 10%--15% relative correction of the effective gate parameters compared to Kerr theory. We find that gate operation is strongly dependent on the ratio of qubit-qubit detuning and anharmonicity. In particular, we characterize five distinct regions of operation, and propose candidate parameter choices for achieving high gate speed and low coherent gate error when the…

The reduced dynamics of an open quantum system obtained from an underlying microscopic Hamiltonian can in general only approximately be described by a time-local master equation. The quality of that approximation depends primarily on the coupling strength and the structure of the environment. Various such master equations have been proposed with different aims. Choosing the most suitable one for a specific system is not straightforward. By focusing on the accuracy of the reduced dynamics we provide a thorough assessment for a selection of methods (Redfield equation, quantum optical master equation, coarse-grained master equation, a related dynamical map approach, and a partial-secular approximation). We consider secondary, here, whether or not an approach guarantees positivity. We use two qubits coupled to a Lorentzian environment in a spin-boson-like fashion modeling a generic situation with various system and bath time scales. We see that, independent of the initial state, the simple Redfield equation with time-dependent coefficients is significantly more accurate than all other…

The uncertainty principle is a striking and fundamental feature in quantum mechanics, distinguishing it from classical mechanics. It offers an important lower bound to predict outcomes of two arbitrary incompatible observables measured on a particle. In quantum information theory, this uncertainty principle is popularly formulized in terms of entropy. Here, we present an improvement of the tripartite quantum-memory-assisted entropic uncertainty relation. The uncertainty's lower bound is derived by considering mutual information and the Holevo quantity. It shows that the bound derived by this method will be tighter than the lower bound of Renes and Boileau [Phys. Rev. Lett. 103, 020402 (2009)]. Furthermore, regarding a pair of mutual unbiased bases as the incompatibility, our bound will become extremely tight for the three-qubit $X$-state system, completely coinciding with the entropy-based uncertainty, and can restore Renes and Boileau's bound with respect to arbitrary tripartite pure states. In addition, by applying our lower bound one can attain the tighter bound of the quantum…

Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The number of terms can become overwhelmingly large for problems at the scale of NISQ hardware that may soon be available. We use unitary partitioning (developed independently by Izmaylov et al. [J. Chem. Theory Comput. 16, 190 (2020)]) to define variational quantum eigensolver procedures in which additional unitary operations are appended to the ansatz preparation to reduce the number of terms. This approach may be scaled to use all coherent resources available after ansatz preparation. We also study the use of asymmetric qubitization to implement the additional coherent operations with lower circuit depth. Using this technique, we find a constant factor speedup for lattice and random Pauli Hamiltonians. For electronic structure Hamiltonians, we prove that linear term reduction with respect to the number of orbitals, which has been previously observed in…

The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)--traceable and self-calibrated method for measuring a microwave-electric-field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between the microwave Rabi frequency and Autler-Townes splitting is more valid and is even more robust against the experimental parameters in the EIA's linear region. Furthermore, a narrower linewidth of cold Rydberg EIA enables us to realize a direct SI-traceable microwave-electric-field measurement as small as $\ensuremath{\sim}100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$.

A recently proposed experimental protocol for quantum gravity induced entanglement of masses (QGEM) requires in principle realizable, but still very ambitious, set of parameters in matter-wave interferometry. Motivated by easing the experimental realization, in this paper, we consider the parameter space allowed by a slightly modified experimental design, which mitigates the Casimir potential between two spherical neutral test masses by separating the two macroscopic interferometers by a thin conducting plate. Although this setup will reintroduce a Casimir potential between the conducting plate and the masses, there are several advantages of this design. First, the quantum gravity induced entanglement between the two superposed masses will have no Casimir background. Secondly, the matter-wave interferometry itself will be greatly facilitated by allowing both the mass ${10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}15}\phantom{\rule{0.28em}{0ex}}\mathrm{kg}$ and the superposition size…

We study the charging process of open quantum batteries mediated by a common dissipative environment in two different scenarios. In the first case, we consider a quantum charger-battery model in the presence of a non-Markovian environment, where the battery can be properly charged in a strong coupling regime, without any external power and any direct interaction with the charger, i.e., a wireless-like charging happens. The environment plays a major role in the charging of the battery, while this does not happen in a weak coupling regime. In the second scenario, we show the effect of individual and collective spontaneous emission rates on the charging process of quantum batteries by considering a two-qubit system in the presence of Markovian dynamics. Our results demonstrate that open batteries can be satisfactorily charged in Markovian dynamics by employing an underdamped regime and/or strong external fields. We also present a robust battery by taking into account subradiant states and an intermediate regime. Moreover, we propose an experimental setup to explore the ergotropy in the…

Molecular quantum simulations with the variational quantum eigensolver (VQE) rely on ansatz states that approximate the molecular ground states. These ansatz states are generally defined by parametrized fermionic excitation operators and an initial reference state. Efficient ways to perform fermionic excitations are vital for the realization of the VQE on noisy intermediate-scale quantum computers. Here, we address this issue by first demonstrating circuits that perform qubit excitations, excitations that do not account for fermionic anticommutation relations. We then extend the functionality of these circuits to perform fermionic excitations. Compared to circuits constructed with the standard use of ``$CNOT$ staircases'', our circuits offer a linear reduction in the number of $CNOT$ gates, by a factor of 2 (8) per single (double) qubit or fermionic excitation, respectively. Our results reduce the requirements for near-term realizations of quantum molecular simulations.

In this paper, the authors develop the theory of impedance matching of scattering waves to finite structures of arbitrary geometry, focusing on modes that have zero reflection back into the input channels at specific frequencies. The framework is applicable to all linear classical wave scattering, and to quantum scattering as long as the scattering potential is short ranged.

The hybrid microwave optomechanical-magnetic system has recently emerged as a promising candidate for coherent information processing because of the ultrastrong microwave photon-magnon coupling and the long life of the magnon and phonon. As a quantum information processing device, the realization of single excitation holds special meaning for the hybrid system. In this paper, we introduce a single two-level atom into the optomechanical-magnetic system and show that an unconventional blockade due to destructive interference cannot offer a blockade of both the photon and magnon. Meanwhile under the condition of single excitation resonance, the blockade of the photon, phonon, and magnon can be achieved simultaneously even in a weak optomechanical region, but the phonon blockade still requires the cryogenic temperature condition.

The semiconductor Bloch equations (SBEs) are routinely used for simulations of strong-field laser-matter interactions in condensed matter. In systems without inversion or time-reversal symmetries, the Berry connections and transition dipole phases (TDPs) must be included in the SBEs, which in turn requires the construction of a smooth and periodic structure gauge for the Bloch states. Here, we illustrate a general approach for such a structure-gauge construction for topologically trivial systems. Furthermore, we investigate the SBEs in the length and velocity gauges and discuss their respective advantages and shortcomings for the high-harmonic generation (HHG) process. We find that in cases where we require dephasing or separation of the currents into interband and intraband contributions, the length-gauge SBEs are computationally more efficient. In calculations without dephasing and where only the total current is needed, the velocity-gauge SBEs are structure-gauge independent and are computationally more efficient. We employ two systems as numerical examples to highlight our…

We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to…

We study tunable optomechanically induced transparency by controlling the dark-mode effect induced by two mechanical modes coupled to a common cavity field. This is realized by introducing a phase-dependent phonon-exchange interaction, which is used to form a loop-coupled configuration. Combining this phase-dependent coupling with the optomechanical interactions, the dark-mode effect can be controlled by the quantum interference effect. In particular, the dark-mode effect in this two-mechanical-mode optomechanical system can lead to a double-amplified optomechanically induced transparency (OMIT) window and a higher efficiency of the second-order sideband in comparison with the standard optomechanical system. This is because the effective mechanical decay rate related to the linewidth of the OMIT window becomes a twofold increase in the weak-coupling limit. When the dark-mode effect is broken, controllable double transparency windows appear and the second-order sideband, as well as the light delay or advance, is significantly enhanced. For an $N$-mechanical-mode optomechanical…

Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. We construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and $M$-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an…

It is widely recognized that entanglement generation and dynamical chaos are intimately related in semiclassical models via the process of decoherence. In this paper, we propose a unifying framework which directly connects the bipartite and multipartite entanglement growth to the quantifiers of classical and quantum chaos. In the semiclassical regime, the dynamics of the von Neumann entanglement entropy, the spin squeezing, the quantum Fisher information, and the out-of-time-order square commutator are governed by the divergence of nearby phase-space trajectories via the local Lyapunov spectrum, as suggested by previous conjectures in the literature. General analytical predictions are confirmed by detailed numerical calculations for two paradigmatic models, relevant in atomic and optical experiments, which exhibit a regular-to-chaotic transition: the quantum kicked top and the Dicke model.

As an energy storing and converting device near atomic size, a quantum battery (QB) promises enhanced charging power and extractable work using quantum resources. However, the ubiquitous decoherence causes its cyclic charging-storing-discharging process to become deactivated, which is called aging of the QB. Here, we propose a mechanism to overcome the aging of a QB. It is found that the decoherence of the QB is suppressed when two Floquet bound states (FBSs) are formed in the quasienergy spectrum of the total system consisting of the QB-charger setup and their respective environments. As long as either the quasienergies of the two FBSs are degenerate or the QB-charger coupling is large in the presence of two FBSs, the QB exposed to the dissipative environments returns to its near-ideal cyclic stage. Our result supplies an insightful guideline to realize the QB in practice using Floquet engineering.

Structured light, as a general term for arbitrary states of amplitude, phase, and polarization in optical fields, is highly topical because of a myriad of applications it has fostered. A geometric description to graphically group classes of structured light has obvious benefits, with some notable advances in analogous Poincar\'e sphere (PS) mapping for both spin and orbital angular momentum (OAM), as well as ray-optical PS approaches for propagation-invariant fields, but all limited in dimensionality they can describe. Here we propose a generalized SU(2) PS for arbitrary dimensional structured light. The states on it represent extended families of beams with multidimensional ray-wave structures, accurately described by SU(2) symmetry groups. We outline how to construct this mapping theoretically, revealing insights into mode transformations involving OAM and geometric phase, and fully verify its efficacy experimentally. The generality of our approach is evident by the reduction to prior PS representations as special cases. We also demonstrate an extension of our approach to explain…

We analyze neutral atom Rydberg ${C}_{Z}$ gates based on adiabatic pulses applied symmetrically to both atoms. Analysis with smooth pulse shapes and Cs atom parameters predicts the gates can create Bell states with fidelity $\mathcal{F}>0.999$ by using adiabatic rapid passage pulses. With globally optimized adiabatic pulse shapes, in a two-photon excitation process, we generate Bell states with fidelity $\mathcal{F}=0.997$. The analysis fully accounts for spontaneous emission from intermediate and Rydberg states, including the Rydberg lifetime in a room-temperature environment, but does not include errors arising from laser noise. The gate protocols do not require individual addressing and are shown to be robust against Doppler shifts due to atomic motion.

A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation for the system and the modes may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly…

Recent studies of quantum circuit models have theoretically shown that frequent measurements induce a transition in a quantum many-body system, which is characterized by a change in the scaling law of the entanglement entropy from a volume law to an area law. In order to propose a way to experimentally observe this measurement-induced transition, we present numerical analyses using matrix-product states on the quench dynamics of a dissipative Bose-Hubbard model with controllable two-body losses, which has been realized in recent experiments with ultracold atoms. We find that when the strength of dissipation increases, there occurs a measurement-induced transition from volume-law scaling to area-law scaling with a logarithmic correction in a region of relatively small dissipation. We also find that the strong dissipation leads to a revival of the volume-law scaling due to a continuous quantum Zeno effect. We show that dynamics starting with the area-law states exhibits strong suppression of particle transport stemming from ergodicity breaking, which can be used in experiments to…

A family of solitons in fourth-order dispersive Kerr media is predicted and thoroughly analyzed. The found solutions unify many previously known classes of solitons, and present favorable characteristics for the dispersion engineering of ultrafast soliton lasers.

The authors describe the capability of an atom-by-atom assembler to create large arrays of neutral atoms and provide an overview of advances that can be realized through several new sorting algorithms, including one that enables the assembly of arbitrary, nonregular target arrays. The performance of the enhanced assembler is then demonstrated experimentally.

We present improved results of sending-or-not-sending twin-field quantum key distribution by using error rejection through two-way classical communications. Our error rejection method, especially our method of actively odd-parity pairing (AOPP) can drastically improve the performance of sending-or-not-sending twin-field protocol in both secure distance and key rate. Taking a typical experimental parameter setting, our method here improves the secure distance by 70 km to more than 100 km in comparison with the prior art results. Comparative study also shows advantageous in key rates at regime of long distance and large misalignment error rate for our method here. The numerical results show that our method here can significantly exceed the absolute limit of direct transmission key rate, and also have an advantageous key rates higher than various prior art results by 10 to 20 times.

Gaussian boson samplers (GBSs) have initially been proposed as a near-term demonstration of classically intractable quantum computation. We show here that they have a potential practical application: Samples from these devices can be used to construct a feature vector that embeds a graph in Euclidean space, where similarity measures between graphs---so-called graph kernels---can be naturally defined. This is crucial for machine learning with graph-structured data, and we show that the GBS-induced kernel performs remarkably well in classification benchmark tasks. We provide a theoretical motivation for this success, linking the extracted features to the number of $r$ matchings in subgraphs. Our results contribute to a new way of thinking about kernels as a quantum hardware-efficient feature mapping, and lead to a promising application for near-term quantum computing.

We investigate the absorption and transmission properties of a weak probe field under the influence of a strong control field in a cavity magnomechanical system. The system consists of two ferromagnetic-material yttrium iron garnet (YIG) spheres coupled to a single cavity mode. In addition to two magnon-induced transparencies (MITs) that arise due to magnon-photon interactions, we observe a magnomechanically induced transparency (MMIT) due to the presence of nonlinear magnon-phonon interaction. We discuss the emergence of Fano resonances and explain the splitting of a single Fano profile to double and triple Fano profiles due to additional couplings in the proposed system. Moreover, by considering a two-YIG system, the group delay of the probe field can be enhanced by one order of magnitude as compared with a single-YIG magnomechanical system. Furthermore, we show that the group delay depends on the tunability of the coupling strength of the first YIG with respect to the coupling frequency of of the second YIG, and vice versa. This helps to achieve larger group delays for weak…

Continuous-variable quantum key distribution (CV-QKD) provides an effective way to obtain the high secret key rate, but is limited by practical techniques. To overcome this limitation, we investigate the performance of CV-QKD protocols when non-Gaussian operations are applied to both sides of the channels, including photon subtraction and addition, and photon catalysis. A comparison is also made between Gaussian modulation and non-Gaussian modulation. We show that the optimal transmission distance cannot be improved by non-Gaussian modulation at the sender's side, but it can be improved by single-photon catalysis at the receiver's side. For a given modulation variance that exceeds a certain threshold, the performance of the zero-photon catalysis at the sender's side is the best when compared with other non-Gaussian modulations (except single-photon catalysis at the receiver's side), and it can always reach the optimal distance. Our paper will provide a useful insight for the use of non-Gaussian modulation to other CV-QKD protocols.

We study multiphoton blockade and photon-induced tunneling effects in the two-photon Jaynes-Cummings model, where a single-mode cavity field and a two-level atom are coupled via a two-photon interaction. We consider both the cavity-field-driving and the atom-driving cases and find that single-photon blockade and photon-induced tunneling effects can be observed when the cavity mode is driven, while the two-photon blockade effect appears when the atom is driven. For the atom-driving case (the two-photon transition process), we present a criterion of the correlation functions for the multiphoton blockade effect. Specifically, we show that quantum interference can enhance the photon blockade effect in the single-photon cavity-field-driving case. Our results are confirmed by analytically and numerically calculating the correlation function of the cavity-field mode. Our work has potential applications in quantum information processing and paves the way for the study of multiphoton quantum coherent devices.

The quantum coupling of individual superconducting qubits to microwave photons leads to remarkable experimental opportunities. Here we consider the phononic case where the qubit is coupled to an electromagnetic surface acoustic wave antenna that enables supersonic (electromagnetic) propagation of the qubit oscillations. This can be considered as a giant atom that is many phonon wavelengths long. We study an exactly solvable toy model that captures these effects, and find that this non-Markovian giant atom has a suppressed relaxation, so long as an effective vacuum coupling exists between a qubit excitation and a localized wave packet of sound, even in the absence of a cavity for the sound waves. Finally, we consider practical implementations of these ideas in current surface acoustic wave devices.

In this paper we derive and discuss the completely spin- and photon-polarization-dependent probability rates for nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. The locally constant field approximation, which is essential for applications in plasma-QED simulation codes, is rigorously derived from the strong-field QED matrix elements in the Furry picture for a general plane-wave background field. We discuss important polarization correlation effects in the spectra of both processes. Asymptotic limits for both small and large values of $\ensuremath{\chi}$ are derived and their spin and polarization dependence is discussed.

Solving linear differential equations (LDEs) is a hard problem for classical computers, while quantum algorithms have been proposed to be capable of speeding up the calculation. However, they are yet to be realized in experiment as it cannot be easily converted into an implementable quantum circuit. Here, we present and experimentally realize an implementable gate-based quantum algorithm for efficiently solving the LDE problem: given an $N\ifmmode\times\else\texttimes\fi{}N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\mathbf{b}$, and an initial vector $\mathbf{x}(0)$, we obtain a target vector $\mathbf{x}(t)$ as a function of time $t$ according to the constraint $d\mathbf{x}(t)/dt=\mathcal{M}\mathbf{x}(t)+\mathbf{b}$. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances, and a gate-based quantum circuit is produced which is friendly to the experimentalists and implementable in current quantum techniques. In addition, we experimentally solve a $4\ifmmode\times\else\texttimes\fi{}4$ linear differential equation using…

We propose to use the steered quantum coherence (SQC) as a signature of quantum phase transitions (QPTs). By considering various spin chain models, including the transverse-field Ising model, $\mathit{XY}$ model, and $\mathit{XX}$ model with three-spin interaction, we showed that the SQC and its first-order derivative succeed in signaling different critical points of QPTs. In particular, the SQC method is effective for any spin pair chosen from the chain, and the strength of SQC, in contrast to entanglement and quantum discord, is insensitive to the distance (provided it is not very short) of the tested spins, which makes it convenient for practical use as there is no need for careful choice of two spins in the chain.

We examine continuous-variable gate teleportation using entangled states made from pure product states sent through a beam splitter. We show that such states are Choi states for a (typically) nonunitary gate, and we derive the associated Kraus operator for teleportation, which can be used to realize non-Gaussian, nonunitary quantum operations on an input state. With this result, we show how gate teleportation is used to perform error correction on bosonic qubits encoded using the Gottesman-Kitaev-Preskill (GKP) code. This result is presented in the context of deterministically produced macronode cluster states, generated by constant-depth linear optical networks, supplemented with a probabilistic supply of GKP states. The upshot of our technique is that state injection for both gate teleportation and error correction can be achieved without active squeezing operations---an experimental bottleneck for quantum optical implementations.

We derive an approximation to QED effects in intense laser fields which can be employed in laser-particle collisions. Treating the laser as a plane wave of arbitrary intensity, we split the wave into fast (carrier) and slow (envelope) modes. We solve the interaction dynamics exactly for the former while performing a local expansion in the latter. This yields a ``locally monochromatic'' approximation (LMA), which we apply to nonlinear Compton scattering in circularly and linearly polarized backgrounds and to nonlinear Breit-Wheeler pair production. We provide the explicit link between the LMA and QED, and benchmark against exact QED results. The LMA is particularly useful for high-energy, intermediate-intensity collisions, where, unlike the ``locally constant field'' approximation, the LMA correctly describes the position and amplitude of harmonic features and exactly reproduces the low energy limit. We show that in the limit of high-intensity and large harmonic order, the locally constant field approximation is recovered from the LMA.

It is expected that the quantum advantage of certain classification problems, like quantum-enhanced machine learning algorithms, will become more pronounced as the Hilbert-space dimension grows, but care must be taken with perturbations on the system, as they lead to security breaches that can be explored by untrusted parties. Here it is shown that the amount of perturbation needed for an adversary to induce a misclassification scales inversely with the dimensionality of the space, but security can be restored if we restrict the class of states to be classified.

We investigate the behavior of two coupled nonlinear photonic cavities, in the presence of inhomogeneous coherent driving and local dissipations. By solving numerically the quantum master equation, either by diagonalizing the Liouvillian superoperator or by using the approximated truncated Wigner approach, we extrapolate the properties of the system in a thermodynamic limit of large photon occupation. When the mean-field Gross-Pitaevskii equation predicts a unique parametrically unstable steady-state solution, the open quantum many-body system presents highly nonclassical properties and its dynamics exhibits the long-lived Josephson-like oscillations typical of dissipative time crystals, as indicated by the presence of purely imaginary eigenvalues in the spectrum of the Liouvillian superoperator in the thermodynamic limit.

We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm for which the quantum circuit structures used usually break the Hamiltonian symmetry. The symmetry-adapted VQE scheme introduced here simply applies the projection operator, which is Hermitian but not unitary, to restore the spatial symmetry in a desired irreducible representation of the spatial group. The entanglement of a quantum state is still represented in a quantum circuit but the nonunitarity of the projection operator is treated classically as postprocessing in the VQE framework. By numerical simulations for a spin-$1/2$ Heisenberg model on a one-dimensional ring, we demonstrate that the symmetry-adapted VQE scheme with a shallower quantum circuit can achieve significant improvement in terms of the fidelity of the ground state and has a great advantage in terms of the ground-state energy with decent accuracy, as compared to the non-symmetry-adapted VQE scheme. We also demonstrate that the present scheme can approximate low-lying excited states that can be…

We present a theoretical and experimental investigation of a diffractive optical element---a generalized spiral phase plate (GSPP) with a transmission function of $\mathrm{exp}[ig(\ensuremath{\varphi})]$, where $g(\ensuremath{\varphi})$ is an unambiguous function. In contrast to the conventional spiral phase plate that is widely used for the generation of ring-shaped vortex beams with an orbital angular momentum (OAM), the GSPP can be used for the generation of nonring (including spiral-shaped) laser beams with a helical wave front. Some examples of the function $g(\ensuremath{\varphi})$ were investigated in detail, showing the features arising in these cases. The proposed GSPP demonstrates angle-dependent distortion resistance properties, whereby for different angular positions of an opaque obstacle on the surface of the element, different values of root-mean-square error are obtained. The angular harmonics spectra of the generated vortex light fields strongly depend on the growth rate of the function $g(\ensuremath{\varphi})$. In addition, the OAM density of the generated nonring…

Square-root topological insulators are recently proposed intriguing topological insulators, where the topologically nontrivial nature of Bloch wave functions is inherited from the square of the Hamiltonian. In this paper, we propose that higher-order topological insulators can also have their square-root descendants, which we term square-root higher-order topological insulators. There, emergence of in-gap corner states is inherited from the squared Hamiltonian which hosts higher-order topology. As an example of such systems, we investigate the tight-binding model on a decorated honeycomb lattice, whose squared Hamiltonian includes a breathing kagome-lattice model, a well-known example of higher-order topological insulators. We show that the in-gap corner states appear at finite energies, which coincides with the nontrivial bulk polarization. We further show that the existence of in-gap corner states results in characteristic single-particle dynamics; namely, setting the initial state to be localized at the corner, the particle stays at the corner even after a long time. Such…

Polar molecules are an emerging platform for quantum technologies based on their long-range electric dipole--dipole interactions, which open new possibilities for quantum information processing and the quantum simulation of strongly correlated systems. Here, we use magnetic and microwave fields to design a fast entangling gate with $>0.999$ fidelity and which is robust with respect to fluctuations in the trapping and control fields and to small thermal excitations. These results establish the feasibility to build a scalable quantum processor with a broad range of molecular species in optical-lattice and optical-tweezers setups.

The interplay among topology, disorder, and non-Hermiticity can induce some exotic topological and localization phenomena. Here we investigate this interplay in a two-dimensional non-Hermitian disordered Chern-insulator model with two typical kinds of non-Hermiticities, the nonreciprocal hopping and on-site gain-and-loss effects. The topological phase diagrams are obtained by numerically calculating two topological invariants in the real space, which are the disorder-averaged open-bulk Chern number and the generalized Bott index, respectively. We reveal that the nonreciprocal hopping (the gain-and-loss effect) can enlarge (reduce) the topological regions and the topological Anderson insulators induced by disorders can exist under both kinds of non-Hermiticities. Furthermore, we study the localization properties of the system in the topologically nontrivial and trivial regions by using the inverse participation ratio and the expansion of single-particle density distribution.

Spontaneous symmetry breaking can occur in the powers of two optical modes coupled into a ring resonator, described by a pair of coupled Lorentzian equations, and featuring tunable self- and cross-phase modulation terms. Investigated is a wide variety of nonlinear materials by changing the ratio of the self- and cross-phase interaction coefficients. Static and dynamic effects range from the number and stability of stationary states to the onset and nature of oscillations. Minimal conditions to observe symmetry breaking are provided in terms of the ratio of the self- and cross-phase coefficients, detuning, and input power. Different ratios of the nonlinear coefficients also influence the dynamical regime, where they can induce or suppress bifurcations and oscillations. A generalized description on this kind is useful for the development of all-optical components, such as isolators and oscillators, constructed from a wide variety of optical media in ring resonators.

In state-of-the-art quantum computing platforms, including superconducting qubits and trapped ions, imperfections in the two-qubit entangling gates are the dominant contributions of error to systemwide performance. Recently, a novel two-qubit parametric gate was proposed and demonstrated with superconducting transmon qubits. This gate is activated through rf modulation of the transmon frequency and can be operated at an amplitude where the performance is first-order insensitive to flux noise. In this work we experimentally validate the existence of this ac sweet spot and demonstrate its dependence on white-noise power from room-temperature electronics. With these factors in place, we observe entangling-gate fidelity with coherence-limited performance. An ensemble of repeated observations has a median fidelity of 98.8%, with roughly 10% of observations above 99%.

This paper investigates the performance optimization of optically pumped magnetometers under zero-field parametric modulation. Based on the analytical solutions of the Bloch equation, both longitudinal and transverse modulations are studied experimentally. To estimate the nonuniform polarization distribution of alkali-metal atoms in the vapor cell, an average pumping rate model is proposed. Furthermore, the accuracy of this model and the measurement of the transverse relaxation rate are verified via the agreement between experimental and theoretical values. The results indicate that optimal performance can be achieved by employing a suitable modulation field, the selection of which is related to the modulation index $u$ in the Bessel series and the pump-light intensity. Although both operating modes show similar responses to weak magnetic fields, their effects on pump-light intensity are different due to the means of detecting atomic polarization. An optimal value of the pump-light intensity on the response strength exists in longitudinal modulation. However, with regard to…

A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we present a practical solution to this: We derive a Bayesian multi-parameter quantum bound, construct the optimal measurement when our bound can be saturated for a single shot, and consider experiments involving a repeated sequence of these measurements. Our method properly accounts for the number of measurements and the degree of prior information, and we illustrate our ideas with a qubit sensing network and a model for phase imaging, clarifying the nonasymptotic role of local and global schemes. Crucially, our technique is a powerful way of implementing quantum protocols in a wide range of practical scenarios that tools such as the Helstrom and Holevo Cram\'er-Rao bounds cannot normally access.

We investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalized Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction, approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $\ensuremath{\hbar}$, reflecting the reduction of the global superfluidity. The real-time vortex nucleation in a rotating trap is shown to be triggered, as for a standard condensate, by the softening of the quadrupole mode. For large angular velocities, when the distance between vortices becomes comparable to the interdroplet distance, the vortices are arranged into a honeycomb structure, which coexists with the triangular geometry of the supersolid lattice and persists during the free expansion of the atomic cloud.

We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multiqudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for single-qubit operations.

We introduce the first-principle model describing frequency comb generation in a whispering-gallery-mode microresonator with the backscattering-induced coupling between the counterpropagating waves. The elaborated model provides deep insights and an accurate description of the complex dynamics of nonlinear processes in such systems. We analyze the backscattering impact on the splitting and reshaping of the nonlinear resonances and demonstrate backscattering-induced modulational instability in the normal dispersion regime and subsequent frequency comb generation. We present and discuss features of the soliton comb dynamics induced by the backward wave.

We study the performance of efficient quantum state tomography methods based on neural-network quantum states using measured data from a two-photon experiment. Machine-learning-inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. While the power of these methods has been demonstrated on synthetic data, applications to real experimental data remain scarce. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states, i.e., to positive semidefinite density matrices, greatly improves the quality of the reconstructed states but renders the learning procedure more demanding. Including additional, possibly unjustified, constraints, such as assuming pure states, facilitates learning, but also biases the estimator.

Usually, when investigating exceptional points (EPs) of an open Markovian bosonic system, one deals with spectral degeneracies of a non-Hermitian Hamiltonian (NHH), which can correctly describe the system dynamics only in the semiclassical regime. A recently proposed quantum Liouvillian framework [Minganti et al., Phys. Rev. A 100, 062131 (2019)] enables the complete determination of the dynamical properties of such systems and their EPs (referred to as Liouvillian EPs, or LEPs) in the quantum regime by taking into account the effects of quantum jumps, which are ignored in the NHH formalism. Moreover, the symmetry and eigenfrequency spectrum of the NHH become a part of much larger Liouvillian eigenspace. As such, the EPs of an NHH form a subspace of the LEPs. Here we show that once an NHH of a dissipative linear bosonic system exhibits an EP of a certain finite order $n$, it immediately implies that the corresponding LEP can become of any higher order $m\ensuremath{\ge}n$ defined in the infinite Hilbert space. These higher-order LEPs can be identified by the coherence and spectral…

In this work we investigate quantum-enhanced target detection in the presence of large background noise using multidimensional quantum correlations between photon pairs generated through spontaneous parametric down-conversion. Until now similar experiments have only utilized one of the photon pairs' many degrees of freedom such as temporal correlations and photon number correlations. Here, we utilized both temporal and spectral correlations of the photon pairs and achieved over an order of magnitude reduction to the background noise and in turn significant reduction to data acquisition time when compared to utilizing only temporal modes. We believe this work represents an important step in realizing a practical, real-time quantum-enhanced target detection system. The demonstrated technique will also be of importance in many other quantum sensing applications and quantum communications.

$\mathcal{PT}$ symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken $\mathcal{PT}$-symmetric states in non-Hermitian open systems are described by scattering matrices. A multilayer structure, as a simplest example of the open system, has no certain definition of the scattering matrix, since the output ports can be permuted. The uncertainty in definition of the exceptional points bordering $\mathcal{PT}$-symmetric and $\mathcal{PT}$-symmetry-broken states poses an important problem, because the exceptional points are indispensable in applications such as sensing and mode discrimination. Here we derive the proper scattering matrix from the unambiguous relation between the $\mathcal{PT}$-symmetric Hamiltonian and scattering matrix. We reveal that the exceptional points of the scattering matrix with permuted output ports are not related to the $\mathcal{PT}$ symmetry breaking. Nevertheless, they can be employed for finding a lasing onset as demonstrated in our time-domain calculations and…

Solitons on a finite background, also called breathers, are solutions of the focusing nonlinear Schr\"odinger equation, which play a pivotal role in the description of rogue waves and modulation instability. The breather family includes Akhmediev breathers (AB), Kuznetsov-Ma (KM), and Peregrine solitons (PS), which have been successfully exploited to describe several physical effects. These families of solutions are actually only particular cases of a more general three-parameter class of solutions originally derived by Akhmediev, Eleonskii, and Kulagin [Theor. Math. Phys. 72, 809 (1987)]. Having more parameters to vary, this significantly wider family has the potential to describe many more physical effects of practical interest than its subsets mentioned above. The complexity of this class of solutions prevented researchers to study them deeply. In this paper, we overcome this difficulty and report several effects that follow from more detailed analysis. Namely, we present the doubly periodic solutions and their Fourier expansions. In particular, we outline some striking…

We propose a scheme to generate structured light using a medium consisting of semiconductor quantum dots via four-wave mixing (FWM). We consider a four-level quantum-dot structure where two strong electromagnetic fields couple upper-level biexciton transitions, whereas a weak field is applied to one of the ground-level exciton transitions. A weak signal field is generated, corresponding to a second ground-level exciton transition; thus the overall configuration transforms into a closed-loop diamond-type shape. To realize a spatially dependent modulating quantum-dot medium, we consider strong coupling fields as structured lights and investigate different regions of spatially structured electromagnetically induced transparency via absorption of the generated signal field. The azimuthal phase-dependent modulation of the absorption profile of the generated signal field is the key factor behind the creation of structured light. In addition, we also demonstrate transfer of orbital angular momentum (OAM) of the control beam to the generated beam through the FWM process and study the effect…

Peik and Tamm [Europhys. Lett. 61, 181 (2003)] proposed a nuclear clock based on the isomeric transition between the ground state and the first excited state of thorium-229. This transition was recognized as a potentially sensitive probe of possible temporal variation of the fine-structure constant, $\ensuremath{\alpha}$. The sensitivity to such a variation can be determined from measurements of the mean-square charge radius and quadrupole moment of the different isomers. However, current measurements of the quadrupole moment are yet to achieve an accuracy high enough to resolve nonzero sensitivity. Here we determine this sensitivity using existing measurements of the change in the mean-square charge radius, coupled with the ansatz of constant nuclear density. The enhancement factor for $\ensuremath{\alpha}$ variation is $K=\ensuremath{-}(0.82\ifmmode\pm\else\textpm\fi{}0.25)\ifmmode\times\else\texttimes\fi{}{10}^{4}$. For the current experimental limit, $\ensuremath{\delta}\ensuremath{\alpha}/\ensuremath{\alpha}\ensuremath{\lesssim}{10}^{\ensuremath{-}17}$ per year, the…

Recent experiments have demonstrated the feasibility of exploiting spectral singularities in open quantum and wave systems, so-called exceptional points, for sensors with strongly enhanced response. Here, we study theoretically the influence of classical parametric noise on the performance of such sensors. Within a Lindblad-type formalism for stochastic Hamiltonians we discuss the resolvability of frequency splittings and the dynamical stability of the sensor, and show that these properties are interrelated. Of central importance are the different features of exceptional points in the spectra of the Hamiltonian and the corresponding Liouvillian. Two realistic examples, a parity-time-symmetric dimer and a whispering-gallery microcavity with asymmetric backscattering, illustrate the findings.

The family of $n$-bit Toffoli gates, with the two-bit Toffoli gate as the figurehead, are of great interest in quantum information as they can be used as universal gates and in quantum error correction, among other things. We present a single-step implementation of arbitrary $n$-bit Toffoli gates (up to a local change of basis), based on resonantly driving a single qubit that has a strong Ising coupling to $n$ other qubits. The setup in the two-qubit case turns out to be identical to the universal Barenco gate. The gate time and error are, in theory, independent of the number of control qubits, scaling better than conventional circuit decompositions. We note that our assumptions, namely, strongly coupling $n+1$ qubits and a driving frequency that scales with $n$, may break down for large systems. Still, our protocol could enhance the capabilities of intermediate-scale quantum computers, and we discuss the prospects of implementing our protocol on trapped ions, Rydberg atoms, and superconducting circuits. Simulations of the latter platform show that the Toffoli gate with two control…

We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the most interesting case being that of qubits. For multiple qubits, we find that quantum computation by Clifford gates and Pauli measurements on magic states can be efficiently classically simulated if the quasiprobability distribution of the magic states is non-negative. This provides the so far missing qubit counterpart of the corresponding result [V. Veitch et al., New J. Phys. 14, 113011 (2012)] applying only to odd dimension. Our approach is more general than previous ones based on mixtures of stabilizer states. Namely, all mixtures of stabilizer states can be efficiently simulated, but for any number of qubits there also exist efficiently simulable states outside the stabilizer polytope. Further, our simulation method extends to negative quasiprobability distributions, where it provides probability estimation. The simulation cost is then…

The Rydberg blockade mechanism is now routinely considered for entangling qubits encoded in clock states of neutral atoms. Challenges towards implementing entangling gates with high fidelity include errors due to thermal motion of atoms, laser amplitude inhomogeneities, and imperfect Rydberg blockade. We show that adiabatic rapid passage by Rydberg dressing provides a mechanism for implementing two-qubit entangling gates by accumulating phases that are robust to these imperfections. We find that the typical error in implementing a two-qubit gate, such as the controlled phase gate, is dominated by errors in the single-atom light shift, and that this can be easily corrected using adiabatic dressing interleaved with a simple spin echo sequence. This results in a two-qubit M\o{}lmer-S\o{}rensen gate. A gate fidelity $\ensuremath{\sim}0.995$ is achievable with modest experimental parameters and a path to higher fidelities is possible for Rydberg states in atoms with a stronger blockade, longer lifetimes, and larger Rabi frequencies.

In this paper, we prove a family of Lieb-Robinson bounds for discrete spin systems with long-range interactions. Our results apply for arbitrary $k$-body interactions, so long as they decay with a power law greater than $kd$, where $d$ is the dimension of the system. More precisely, we require that the sum of the norm of terms with diameter greater than or equal to $R$, acting on any one site, decays as a power law $1/{R}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}>d$. These bounds allow us to prove that, at any fixed time, the spatial decay of a time evolved operator follows arbitrarily closely to $1/{r}^{\ensuremath{\alpha}}$. Moreover, we introduce an alternative light cone definition for power-law interacting quantum systems which captures the region of the system where changing the Hamiltonian can affect the evolution of a local operator. In short-range interacting systems, this light cone agrees with the conventional definition. However, in long-range interacting systems, our definition yields a stricter light cone, which is more relevant in most physical contexts.

In the past few decades, many works have been devoted to the study of exceptional points (EPs), i.e., exotic degeneracies of non-Hermitian systems. The usual approach in those studies involves the introduction of a phenomenological effective non-Hermitian Hamiltonian (NHH), where the gain and losses are incorporated as the imaginary frequencies of fields and from which the Hamiltonian EPs (HEPs) are derived. Although this approach can provide valid equations of motion for the fields in the classical limit, its application in the derivation of EPs in the quantum regime is questionable. Recently, a framework [Minganti et al., Phys. Rev. A 100, 062131 (2019)] which allows one to determine quantum EPs from a Liouvillian EP (LEP), rather than from an NHH, has been proposed. Compared to the NHHs, a Liouvillian naturally includes quantum noise effects via quantum-jump terms, thus allowing one to consistently determine its EPs purely in the quantum regime. In this work we study a non-Hermitian system consisting of coupled cavities with unbalanced gain and losses, where the gain is far from…

We study the interaction of laser pulses carrying orbital angular momentum (OAM) with structural asymmetry quantum-dot molecules characterized by four energy levels. We demonstrate how the interdot tunneling endows exchange of optical vortices between different frequencies. We consider a case where a weak probe beam has an optical vortex and thus has a zero intensity at the center. The presence of tunneling coupling generates an additional weak laser beam with the same vorticity as that of the incident vortex beam. We analyze conditions for the vortex of the initial beam to be transferred efficiently to the generated beam. The propagation of Laguerre-Gaussian (LG) beams possessing OAM states characterized by both azimuthal and radial indices is then investigated for the case where the strong control beam is also an OAM mode. It is shown that the conservation of OAM states is always satisfied over the OAM exchange process. Yet, an abnormal case is observed in which the radial index induces some intensity patterns of the generated beam which differs from a pure LG beam of incident…

The second virial coefficient and the second acoustic virial coefficient for helium-4 and helium-3 are computed for a wide range of temperatures (0.5--1000 K) using a highly accurate nonrelativistic interaction potential [M. Przybytek et al., Phys. Rev. Lett. 119, 123401 (2017)] and recalculated relativistic and quantum-electrodynamic components. The effects of the long-range retardation and of the nonadiabatic coupling of the nuclear and electronic motion are also taken into account. The results of our calculations represent at least fivefold improvement in accuracy compared to the previous ab initio work. The computed virial coefficients agree well with the most accurate recent measurements but have significantly smaller uncertainty.

Machine learning has emerged as a promising approach to unveil properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods---such as Monte Carlo---which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data-reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented quantum algorithm recovers. Finally, we propose a majority vote quantum classifier built from a nearest-neighbor (checkerboard) quantum neural…

Developing a unified formalism to describe distillation in a general resource-theoretic setting is challenging. Here, a comprehensive set of tools applicable to broad classes of resource theories is developed, revealing the similarities among many of them and establishing universal limitations on the distillation of such resources in practical settings.

We propose to explore the quantum nature of gravity using the correlation of light between two optomechanical cavities, and the quantumness of the correlation is witnessed by squeezing. As long as the gravity between the end mirrors of two cavities is quantum in the Newtonian limit, we show that the squeezing is always nonzero and monotonically increases as the mechanical property of the mirrors is improved. The proposed scheme provides a new pathway for testing the quantum nature of gravity systematically with tabletop experiments.

Parity meters, utilized to distinguish bipartite quantum states with even or odd parity, have many applications in quantum information processing. We propose a potentially practical scheme to construct the nondestructive Rydberg parity meter (NRPM) in ground-state subspace using Rydberg atoms. Based on the proposed NRPM, the parity of the qubit atoms could be known in a deterministic and nondestructive way, implying that the output state of the NRPM can be further used in the rest of the process for quantum information tasks. In addition, we study the applications of the proposed NRPM in entangled state fusion, entangled state analysis, and quantum teleportation, as well as quantum logic gate in a decoherence-free subspace regarding collective-dephasing errors. We analyze the performance of the NRPM under the influence of decoherence and consider more general situations for the feasibility of the scheme.

We experimentally demonstrate a parametric iswap gate in a superconducting circuit based on a tunable coupler for achieving a continuous tunability to eliminate unwanted qubit interactions. We implement the two-qubit iswap gate by applying a fast-flux bias modulation pulse on the coupler to turn on parametric exchange interaction between computational qubits. The controllable interaction can provide an extra degree of freedom to verify the optimal condition for constructing the parametric gate. Aiming to fully investigate error sources of the two-qubit gates, we perform quantum process tomography measurements and numerical simulations as varying static $ZZ$ coupling strength. We quantitatively calculate the dynamic $ZZ$ coupling parasitizing in two-qubit gate operation, and extract the particular gate error from the decoherence, dynamic $ZZ$ coupling, and high-order oscillation terms. Our results reveal that the main gate error comes from the decoherence, while the increase in the dynamic $ZZ$ coupling and high-order oscillation error degrades the parametric gate performance. This…

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires $O({2}^{{n}_{Q}})$ entangling gates on a quantum computer with ${n}_{Q}$ qubits per site. It is conceivable that instead initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a noninteracting scalar field theory, initializing to a symmetric exponential wave function requires ${n}_{Q}\ensuremath{-}1$ entangling gates, the minimal number necessary to create an entangled state of all ${n}_{Q}$ qubits. This is compared with the ${2}^{{n}_{Q}\ensuremath{-}1}+{n}_{Q}\ensuremath{-}3+{\ensuremath{\delta}}_{{n}_{Q},1}$ required for a symmetric Gaussian wave function. In this work, we explore the initialization of one-site (${n}_{Q}=4$), two-site (${n}_{Q}=3$), and three-site (${n}_{Q}=3$) noninteracting scalar field theories with symmetric exponential wave functions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo).…

It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not interact. Claims to the contrary based on quantum violations of Bell inequalities are argued to be incorrect. A specific example traces a violation of the CHSH Bell inequality in the case of a spin-3/2 particle to the noncommutation of certain quantum operators in a situation where (non)locality is not an issue. A consistent histories analysis of what quantum measurements measure, in terms of quantum properties, is used to identify the basic problem with derivations of Bell inequalities: the use of classical concepts (hidden variables) rather than a probabilistic structure appropriate to the quantum domain. A difficulty with the original Einstein-Podolsky-Rosen (EPR) argument for the incompleteness of quantum mechanics is the use of a counterfactual argument which is not valid if one assumes that Hilbert-space quantum mechanics is complete;…

Ghost imaging is demonstrated using a polyenergetic reactor source of thermal neutrons. This enables position resolution to be incorporated into a variety of neutron instruments that are not position resolving. Such a proof of concept enables several further applications. For example, in an imaging context, neutron ghost imaging can be beneficial for dose reduction and resolution enhancement. We explore the principle of resolution enhancement by employing a variant of the method in which each pixel of a position-sensitive detector is regarded as an independent bucket detector; a neutron ghost image is then computed for each pixel. We demonstrate the principle that this parallel form of neutron ghost imaging can significantly increase the spatial resolution of a pixelated detector such as a CCD or CMOS camera. Further applications and extensions of our neutron ghost-imaging protocol are discussed. These include neutron ghost tomography, neutron ghost microscopy, dark-field neutron ghost imaging, and isotope-resolved color neutron ghost imaging via prompt-gamma-ray bucket detection.

We address a particular instance where open quantum systems may be used as quantum probes for an emergent property of a complex system, as the temperature of a thermal bath. The inherent fragility of the quantum probes against decoherence is the key feature making the overall scheme very sensitive. The specific setting examined here is that of quantum thermometry, which aims to exploit decoherence as a resource to estimate the temperature of a sample. We focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic regime (ranging from sub-Ohmic to super-Ohmic), by using pairs of qubits in different initial states and interacting with different environments, consisting either of a single thermal bath or of two independent ones at the same temperature. Our scheme involves pure dephasing of the probes, thus avoiding energy exchange with the sample and the consequent perturbation of temperature itself. We discuss the role of correlations among the probes and the presence of a local versus a global bath. We show that entanglement improves thermometry at short times if…

We present a variational quantum circuit that produces the singular value decomposition of a bipartite pure state. The proposed circuit, which we name quantum singular value decomposer or QSVD, is made of two unitaries respectively acting on each part of the system. The key idea of the algorithm is to train this circuit so that the final state displays exact output coincidence from both subsystems for every measurement in the computational basis. Such circuit preserves entanglement between the parties and acts as a diagonalizer that delivers the eigenvalues of the Schmidt decomposition. Our algorithm only requires measurements in one single setting, in striking contrast to the ${3}^{n}$ settings required by state tomography. Furthermore, the adjoints of the unitaries making the circuit are used to create the eigenvectors of the decomposition up to a global phase. Some further applications of QSVD are readily obtained. The proposed QSVD circuit allows us to construct a SWAP between the two parties of the system without the need of any quantum gate communicating them. We also show…

We employ the intertwining operator technique to synthesize a supersymmetric (SUSY) array of arbitrary size $N$. The synthesized SUSY system is equivalent to a spin $(N\ensuremath{-}1)/2$ under an effective magnetic field. By considering an additional imaginary magnetic field, we obtain a generalized parity-time-symmetric non-Hermitian Hamiltonian that describes a SUSY array of coupled resonators or waveguides under a gradient gain and loss; all the $N$ energy levels coalesce at an exceptional point (EP), forming an isotropic high-order EP with $N$ states coalescence (EPN). Near the EPN, the scaling exponent of phase rigidity for each eigenstate is $(N\ensuremath{-}1)/2$; the eigenfrequency response to the perturbation $\ensuremath{\epsilon}$ acting on the resonator or waveguide couplings is ${\ensuremath{\epsilon}}^{1/N}$. Our findings reveal the importance of the intertwining operator technique for spectral engineering and exemplify the practical application in non-Hermitian physics.

In this work, we study the transmission of classical information through three completely depolarizing channels in superposition of different causal orders. We exploit the quantum 3-switch as a resource for classical communication. We perform a kind of quantum control that was not accessible to the previously treated two-channel case. The fine and full quantum control achieved using selected combinations of causal orders let us uncover several features: nonmonotonous behavior on the transmission of information with respect to the number of causal orders involved, and different values of the transmission of information depending on the specific combinations of causal orders considered. Our results are a stepping stone to assess the efficiency of coherent quantum control and optimize resources in the implementation of indefinite causal structures. Finally, we suggest an optical implementation using standard telecom technology to test our predictions.

We propose a scheme to demonstrate spatiotemporal-vortex four-wave mixing (FWM) in an asymmetric semiconductor double quantum-well nanostructure. It is found that the orbital-angular-momentum (OAM) phase is transferred entirely from a unique OAM mode to the FWM field. Interestingly, by adjusting the detuning or the intensity of a control field, one can effectively modulate the phase and intensity of the FWM field. Also, we perform the superposition modes created by the interference between the FWM field and a same-frequency Laguerre-Gaussian mode, which show many interesting properties. Moreover, the conversion efficiency and quality of the output FWM field are studied. It is shown that the generated FWM mode has a maximum fidelity of approximately 100%. Our result may find potential applications in fundamental research and quantum technologies based on OAM light in solids.

General relativity is a classical field theory and therefore does not predict gravitationally induced entanglement. As such, recent proposals have focused on seeking an empirical demonstration of this feature. We introduce improvements to a spin witness protocol that reduce the highly challenging experimental requirements. After rigorously assessing approximations from the original proposal [S. Bose et al., Phys. Rev. Lett. 119, 240401 (2017)], we focus on entanglement witnessing. We propose a witness which greatly reduces the required interaction time, thereby making the experiment feasible for higher decoherence rates, and we show how statistical analysis can separate the gravitational contribution from other possibly dominant and ill-known interactions. We point out a potential loophole and show how it can be closed using state tomography.

We propose a continuous-variable quantum secret sharing (CV-QSS) protocol in which the quantum states are prepared passively using a thermal source. In our protocol, one player splits the output of a thermal source into two spatial modes with the help of a beam splitter, then he (or she) measures one of the correlated thermal states and sends the others to the secure station of the adjacent player in sequence after using appropriate optical attenuation, which waives the necessity of employment of high extinction ratio modulators with good stability. Therefore, the proposed protocol provides convenient implementation in QSS framework. Moreover, our scheme is immune to Trojan horse attacks. We derive the security bounds for our protocol against both eavesdroppers and dishonest players. Furthermore, we can achieve tighter bound of QSS distance by considering the finite-size effect, which is more practical than that obtained in the asymptotic limit.

We analyze a notable class of states relevant to an immiscible bosonic binary mixture loaded in a rotating boxlike circular trap, i.e., states where vortices in one species host the atoms of the other species, which thus play the role of massive cores. Within a fully analytical framework, we calculate the equilibrium distance distinguishing the motion of precession of two corotating massive vortices, the angular momentum of each component, the vortices healing length, and the characteristic size of the cores. We then compare these previsions with the measures extracted from the numerical solutions of the associated coupled Gross-Pitaevskii equations. Interestingly, making use of a suitable change of reference frame, we show that vortices drag the massive cores which they host thus conveying their same motion of precession, but that there is no evidence of tangential entrainment between the two fluids, since the cores keep their orientation constant while orbiting.