In this work we study simulations of photon generation due to the dynamical Casimir effect (DCE) in a one-dimensional ($1+1$) double superconducting cavity. To achieve this, we propose the use of a superconducting quantum circuit so as to be able to experimentally perform quantum simulations of the DCE. The simulated cavity consists of two perfectly conducting mirrors and a dielectric membrane of infinitesimal depth that effectively couples two cavities. The total length of the double cavity $L$, the difference in length between the two cavities $\mathrm{\Delta }L$, and the electric susceptibility $\chi$ and conductivity $v$ of the dielectric membrane are tunable parameters. All four parameters are treated as independent and are allowed to be tuned at the same time, even with different frequencies. We analyze the cavity's energy spectra under different conditions, finding a transition between two distinct regimes that is accurately described by $k_c=\sqrt{v/\chi }$. In particular, a lowest-energy mode is forbidden in one of the regimes while it is allowed in the other. We compare analytical approximations obtained through the multiple-scale analysis method with exact numerical solutions, obtaining the typical results when $\chi$ is not being tuned. However, when the susceptibility $\chi$ is tuned, different behaviors (such as oscillations in the number of photons of a cavity prepared in a vacuum state) can arise if the frequencies and amplitudes of all parameters are adequate. These oscillations might be considered as adiabatic shortcuts where all generated photons are eventually destroyed.

We examine the satisfaction of Bell criteria for single realizations of quantum systems. This is possible via the joint noisy measurement of all observables involved in the Bell test. We readily find that every outcome violates Bell bounds for local hidden-variable models. This agrees with the idea that to reveal nonclassical effects a necessary condition is that the measuring scheme itself must be nonclassical.

A standard two-qubit joint measurement is the well-known Bell state measurement, in which each reduced state (traced out one qubit) is the completely mixed state. Recently, a novel quantum joint measurement known as the elegant joint measurement (EJM) has been proposed, where the reduced states of the EJM basis have tetrahedral symmetry. In this paper, we first propose a five-parameter entangled state and reveal its inherent symmetry. Based on this, we define a generalized EJM parametrized by $z$, ${\phi }_{}$, and ${\theta }_{}$, and provide the quantum circuits for preparing and detecting these basis states. There are three main results: (i) The previous single-parameter EJM can be directly derived by specifying the parameters $z$ and ${\phi }_{}$; (ii) the initial unit vectors related to the four vertices of the regular tetrahedron are not limited to the original choice and not all the unit vectors in cylindrical coordinates are suitable for forming the EJM basis; and (iii) the reduced states of the present EJM basis can always form two mirror-image tetrahedra, robustly preserving its elegant properties. We aim to determine what kind of states the EJM basis belongs to and to provide a method for constructing the generalized three-parameter EJM, which may contribute to the multisetting measurement and the potential applications for quantum information processing.

The overlap between quantum measurement operators is a fundamental quantity, and the notion of an equioverlapping measurement captures a symmetric feature of quantum measurements in terms of overlap. Such equioverlapping measurements, as a special class of quantum measurements, interpolate between von Neumann measurements and symmetric informationally complete positive operator-valued measures (SIC-POVMs), and exhibit a rich and subtle structure. In this work, we classify and completely determine all equioverlapping measurements in qubit and qutrit systems.

To obtain Bell statistics from hybrid systems composed of finite- and infinite-dimensional systems, we propose a hybrid measurement scheme, in which the continuous mode is measured using the generalized pseudospin operators, while the finite (two)-dimensional system is measured in the usual Pauli basis. Maximizing the Bell expression with these hybrid measurement settings leads to the violations of local realism in the hybrid system, which is referred to as hybrid nonlocality. We demonstrate the utility of our strategy in a realistic setting of cavity quantum electrodynamics, where an atom interacts resonantly with a single mode of an electromagnetic field under the Jaynes-Cummings Hamiltonian. We dynamically compute the quenched averaged value of hybrid nonlocality in imperfect situations by incorporating disorder in the atom-cavity coupling strength. In the disordered case, we introduce two kinds of measurement scenarios to determine the Bell statistics—in one situation, experimentalists can tune the optimal settings according to the interaction strength, while such controlled power is absent in the other case. In contrast to the oscillatory behavior observed in the ordered case, the quenched averaged violation saturates to a finite value in some parameter regimes in the former case. We also examine the connection between Wigner negativity and hybrid nonlocality.

We address the variational preparation of the thermofield double as the ground state of a suitably engineered Hamiltonian acting on the doubled Hilbert space. Through the use of the Entanglement Forging ansatz, we propose a solution that involves only circuits of width $N$. We illustrate the method with generic fermionic Hamiltonians. The free fermion case can be solved in closed form and yields a warm start state for the variational circuits whenever interactions are present. As an important side product, this method returns the complete energy spectrum and eigenbasis of the system.

Quantum singular-value transformation (QSVT) is a framework that has been shown to unify many primitives in quantum algorithms. In this work we leverage the QSVT framework in two directions. We first show that the QSVT framework can accelerate one recently introduced quantum power method, which substantially improves its running time. Additionally, we incorporate several elementary numerical integration techniques, such as the rectangular method, Monte Carlo method, and quadrature method, into the QSVT framework, which results in polynomial speedup with respect to the size or the number of points of the grid. Our results thus provide further examples to demonstrate the potential of the QSVT and how it may enhance quantum algorithmic tasks.

In recent years, researchers have been exploring the applications of noisy intermediate-scale quantum (NISQ) computation in various fields. One important area in which quantum computation can outperform classical computers is the ground-state problem of a many-body system, e.g., the nucleus. However, using a quantum computer in the NISQ era to solve a meaningful-scale system remains a challenge. To calculate the ground energy of nuclear systems, we propose a new algorithm that combines classical shadow and subspace diagonalization techniques. Our subspace is composed of matrices, with the basis of the subspace being the classical shadow of the quantum state. We test our algorithm on nuclei described by the Cohen-Kurath shell model and USD shell model. We find that the accuracy of the results improves as the number of shots increases, following the Heisenberg scaling.

Hybrid quantum systems consisting of quantum dot spins and superconducting circuits have emerged as a promising platform for quantum information processing. However, the development of scalable architectures requires the ability to entangle different quantum systems over long distances, which remains an outstanding challenge for hybrid systems with complex interactions and multiple energy levels. Here, we devise methods to implement entangling gates by using engineered virtual photons as a transducer to couple spin-superconducting systems. We propose to tailor such transducers by tuning the driving pulse using shortcuts to adiabaticity. We demonstrate the realization of high-fidelity entangling gates of 99% in short timescales of a few tens of nanoseconds, and we show the robustness of this approach to control parameters. Furthermore, our method enables state transfer and remote entanglement between different modules of the hybrid system with fidelity exceeding the fault-tolerance threshold, thus demonstrating the scalability of this approach. These results pave the way for fast, high-fidelity quantum information processing on leading hybrid platforms.

Quantum reservoirs have great potential as they utilize the complex real-time dissipative dynamics of quantum systems for information processing and target time-series generation without precise control or fine-tuning of the Hamiltonian parameters. Nonetheless, their realization is challenging as quantum hardware with appropriate dynamics, robustness to noise, and ability to produce target steady states is required. To that end, we propose the disordered quantum homogenizer as an alternative interaction model, and prove it satisfies the necessary and sufficient conditions (stability and contractivity) of the reservoir dynamics, necessary for solving machine learning tasks with time-series input data streams. The results indicate that the quantum homogenization protocol, physically implementable as either nuclear magnetic resonance ensemble or a photonic system, can potentially function as a reservoir computer.

Thouless pumping with nontrivial topological phases provides a powerful means for the manipulation of matter waves in one-dimensional lattice systems. The band topology is revealed by the quantization of pumped charge. In the context of Thouless pumping, we present a graphical representation for the topological phases characterized by the Chern number of an effective two-dimensional band. We illustrate how two topological phases with a distinct Zak phase are connected in the pumping process. Such a visual depiction exhibits typical patterns that is directly related to a linking number and to the Chern number, allowing for the construction of Thouless pumping schemes in a practical way. As a demonstration, we present a generalized Creutz model with a tunable Peierls phase, interleg imbalance, and diagonal hopping. Various modulation schemes for Thouless pumping are studied, focusing on their graphical representations in Bloch space, as well as the quantized pumping phenomenon in real space.

Lieb excitations are fundamental to the understanding of the low-energy behavior of many-body quantum gases. Here we study the spectral function of a Tonks-Girardeau gas in a finite-sized Kronig-Penney potential and show that the Lieb-I and Lieb-II excitations can become gapped as a function of the barrier height. Moreover, we reveal the existence of a topological flat mode near the Fermi energy and at zero momentum and show that this is robust to perturbations in the system. Through a scaling analysis, we determine the divergent behavior of the spectral function. Our results provide a significant reference for the observation and understanding of the gapped Lieb excitations and the topological flat mode of quantum gases in experimentally realistic subwavelength optical lattice potentials.

Long-range dipolar effects in one-dimensional (1D) systems, either in free or inhomogeneous space, are the basis of the state preparation protocol here proposed. Under the presence of an external time-dependent magnetic field, dipole-dipole interactions in the binary ultracold ${}^{166}\mathrm{Er}$ -${}^{164}\mathrm{Dy}$ system were tuned from repulsive to attractive to access either the droplet regime or the cloud one filling the full space, where individual species can be found in mixed or demixed phases. A thorough exploration of weak contact and dipole-dipole effective interaction parameters leads us to determine the phase diagrams of the 1D Bose clouds affected by three different external fields: free homogeneous, harmonic, and optical lattice confining potentials. These results were used to propose long-life states composed of alternate assemblies of individual species confined in optical lattices that mimics magnetic domains, whose size can be adjusted. Our analysis, based on numerical experiments within a mean-field scheme, considered large enough systems as those commonly used in experimental platforms.

In cavity magnomechanics, we find that the unique ultrastrong magnon-microwave photon interaction can induce mode competition in multimode phonon lasers, even though each mechanical mode is coupled to its respective driven magnon mode, which plays the similar role of the gain medium in the optical laser. Such a separate model corresponds to a richer phase diagram compared to that in which all modes are immersed in a common gain medium, in particular containing a second-order phase transition: the excited oscillator changes its behavior from suppression to absorption of the other oscillator's energy, leading to an obvious cooling by heating phenomenon. The mode competition phase transition also has a good correspondence with the synchronization phenomenon between the self-sustaining dynamics of the phonon modes. Finally, we discuss that the mode competition will be weakened as more modes are present in the system. Our work provides a foundation for related studies such as the self-sustaining dynamics of multibodies with complex structures.

The interaction of atoms with higher-order Poincaré optical vortex modes of order $m\ge 0$ is explored for light close to resonance with atomic dipole transitions. It is well known that atoms subject to optical vortex modes experience both translational and rotational forces acting on the atomic center of mass, leading to atom dynamics and atom trapping. Here we consider the optical forces on atoms immersed in general paraxial higher-order Poincaré optical vector modes. The coupling to atoms gives rise to wide-ranging scenarios involving such modes in which any specific polarization is within a spectrum of wave polarization and all the interactions are treatable within a single formulation. We show that this gives rise to a variety of physical situations, governed by the mode order $m$, the polarization represented by the angular coordinates of the mode on the surface of the unit Poincaré sphere, the atomic transitions involved, and their selection rules. We present the analytical steps leading to the optical forces on sodium atoms and display their variations in various situations.

We show how to entangle the motion of optically levitated nanoparticles in distant optical tweezers. The scheme consists in coupling the inelastically scattered light of each particle into transmission lines and directing it towards the other particle. The interference between this light and the background field introduces an effective coupling between the two particles while simultaneously reducing the effect of recoil heating. We analyze the system dynamics, showing that both transient and conditional entanglement between remote particles can be achieved under realistic experimental conditions.

Path-entangled optical photons have played an important role in the multinode quantum network and quantum sensing, although most of them were usually generated probabilistically with linear optical platforms. Here, by using the spontaneous radiations of a pair of entangled solid-state qubits coupled to a common one-dimensional waveguide, we alternatively propose an on-chip approach to deterministically generate the path-entangled microwave single-photon state. With the trapped electrons on liquid helium, we specifically demonstrate its feasibility. In addition to the calculation of the von Neumann entropy for the entanglement witness, we show that the generated path-entanglement photons can be experimentally tested by simply measuring the distinguishability of the spontaneously emitted spectra of the photons being detected by the left and right single-photon detectors. The generalization of the proposal to the other solid-state experimental platforms is also discussed.

We theoretically propose a scheme for achieving nonreciprocal bipartite and tripartite entanglement among magnons, photons, and phonons utilizing the Barnett effect in a cavity magnomechanical (CMM) system where a rotating yttrium iron garnet sphere is placed in a microwave cavity. The Barnett effect induces a Barnett frequency shift that can be effectively controlled to be either positive or negative by adjusting the direction of the magnetic field. As a result, nonreciprocal bipartite and tripartite entanglement can be achieved, exhibiting robustness against the bath temperature. Our work provides a very accessible way to manipulate photon-magnon-phonon quantum resources based on CMM devices with the Barnett effect.

A major thrust in quantum algorithm development over the past decade has been the search for the quantum algorithms that will deliver practical quantum advantage first. Today's quantum computers—and even early fault-tolerant quantum computers—are limited in the number of operations they can implement per circuit. We introduce quantum algorithms for ground-state-energy estimation (GSEE) that accommodate this design constraint. The first algorithm estimates ground-state energies, offering a quadratic improvement on the ground-state overlap parameter compared to other methods in this regime. The second algorithm certifies that the estimated ground-state energy is within a specified error tolerance of the true ground-state energy, addressing the issue of gap estimation that beleaguers several ground-state preparation and energy estimation algorithms. We note, however, that the scaling of this certification technique is currently less favorable than that of the GSEE algorithm. To develop the certification algorithm, we propose an alternative use of quantum computers to facilitate rejection sampling. After a classical computer generates initial samples, the quantum computer is used to accept or reject these samples, resulting in a set of accepted samples that approximate draws from a target distribution. Although we apply this technique specifically for ground-state-energy certification, it may find broader applications. Our paper pushes the boundaries of what operation-limited quantum computers can achieve, bringing the prospect of quantum advantage closer to realization.