Probabilistic hysteresis is a manifestation of irreversibility in a small dissipationless classical system [R. Bürkle et al., Sci. Rep. 9, 14169 (2019)]: After a slow cyclic sweep of a control parameter, the probability that an initial microcanonical ensemble returns to the neighborhood of its initial energy is significantly below one. A similar phenomenon has recently been confirmed in a corresponding quantum system, when the particle number $N$ is not too small. Quantum-classical correspondence has been found to be nontrivial in this case however; the rate at which the control parameter changes must not be extremely slow and the initial distribution of energies must not be too narrow. In this paper we directly compare the quantum and classical forms of probabilistic hysteresis by making use of the Husimi quantum-phase-space formalism. In particular, we demonstrate that the classical ergodization mechanism, which is a key ingredient in classical probabilistic hysteresis, can lead to a breakdown of quantum-classical correspondence rather than to quantum ergodization. Such quantum failure of ergodization leads to strong quantum effects on the long-term evolution even when the quantum corrections in the equations of motion, which are proportional to $1/N$, would naively seem to be small. We also show, however, that quantum ergodization can be restored by averaging over energies, so that for not-too-narrow initial energy width and not-too-slow parameter change the classical results are recovered after all at large $N$. Finally, we show that the formal incommutability of the classical and adiabatic limits in our system, which is responsible for the breakdown of quantum-classical correspondence in the quasistatic limit, is due to macroscopic quantum tunneling through a large energetic barrier. This explains the extremely slow sweep rates needed to reach the quantum adiabatic limit that were reported in our previous work. The formal incommutability therefore has no consequences for any realistically slow sweeps unless $N$ is quite small ($N\lesssim 20$).

We use geometric concepts originally proposed by Anandan and Aharonov [Phys. Rev. Lett. 65, 1697 (1990)] to show that the Farhi-Gutmann time-optimal analog quantum search evolution between two orthogonal quantum states is characterized by unit efficiency dynamical trajectories traced on a projective Hilbert space. In particular, we prove that these optimal dynamical trajectories are the shortest geodesic paths joining the initial and the final states of the quantum evolution. In addition, we verify they describe minimum uncertainty evolutions specified by an uncertainty inequality that is tighter than the ordinary time-energy uncertainty relation. We also study the effects of deviations from the time-optimality condition from our proposed Riemannian geometric perspective. Furthermore, after pointing out some physically intuitive aspects offered by our geometric approach to quantum searching, we mention some practically relevant physical insights that could emerge from the application of our geometric analysis to more realistic time-dependent quantum search evolutions. Finally, we briefly discuss possible extensions of our paper to the geometric analysis of the efficiency of thermal trajectories of relevance in quantum computing tasks.

The implementation and practicality of quantum algorithms hinge largely on the quality of operations within a quantum processor. Therefore, including realistic error models in quantum computing simulation platforms is crucial for testing these algorithms. Existing classical simulation techniques of quantum information processing devices exhibit a tradeoff between scalability (the number of qubits that can be simulated) and accuracy (how close the simulation is to the target error model). In this paper, we introduce a simulation approach that relies on approximating the density matrix evolution with a stochastic sum of unitary and measurement channels within a pure-state simulation environment. This model shows an improvement of at least one order of magnitude in terms of accuracy compared to the best known stochastic approaches while allowing us to simulate a larger number of qubits compared to the exact density matrix simulation. Furthermore, we used this approach to realistically simulate Grover's algorithm and the surface code 17 using a gate set tomography characterization of quantum operations as a noise model.

Trapped ions are sensitive detectors of weak forces and electric fields that excite ion motion. Here measurements of the center-of-mass motion of a trapped-ion crystal that are phase coherent with an applied weak external force are reported. These experiments are conducted far from the trap motional frequency on a two-dimensional trapped-ion crystal of approximately 100 ions, and determine the fundamental measurement imprecision of our protocol free from noise associated with the center-of-mass mode. The driven sinusoidal displacement of the crystal is detected by coupling the ion crystal motion to the internal spin degree of freedom of the ions using an oscillating spin-dependent optical dipole force. The resulting induced spin precession is proportional to the displacement amplitude of the crystal, and is measured with near-projection-noise-limited resolution. A $49\mathrm{pm}$ displacement is detected with a signal-to-noise ratio of 1 in a single experimental determination, which is an order-of-magnitude improvement over prior phase-incoherent experiments. This displacement amplitude is 40 times smaller than the zero-point fluctuations. With our repetition rate, an $8.4\mathrm{pm}/\sqrt{\mathrm{Hz}}$ displacement sensitivity is achieved, which implies $12(\mathrm{yN}/\mathrm{ion})/\sqrt{\mathrm{Hz}}$ and $77(\mu \mathrm{V}/\mathrm{m})/\sqrt{\mathrm{Hz}}$ sensitivities to forces and electric fields, respectively. This displacement sensitivity, when applied on-resonance with the center-of-mass mode, indicates the possibility of weak force and electric field detection below ${10}^{-3}\mathrm{yN}$/ion and $1\mathrm{nV}$/m, respectively.

Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available numerical methods, in particular those based on variational Monte Carlo simulations, become exponentially more challenging with increasing system size. Recently quantum algorithms implemented as variational models have been proposed to accelerate such simulations. The variational ansatz states are characterized by a polynomial number of parameters devised in a way to minimize the expectation value of a given Hamiltonian, which is emulated by local measurements. In this study, we develop a means to certify the termination of variational algorithms. We demonstrate our approach by applying it to three models: the transverse field Ising model, the model of one-dimensional spinless fermions with competing interactions, and the Schwinger model of quantum electrodynamics. By means of comparison, we observe that our approach shows better performance near critical points in these models. We hence take a further step to improve the applicability and to certify the results of variational quantum simulators.

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 $\chi$ are derived and their spin and polarization dependence is discussed.

The energies of the lowest ${}^{2}P_u$, ${}^{4}P_g$, and $2D_g$ states of the boron atom are calculated with $\mu \mathrm{hartree}$ accuracy, in the basis of symmetrized, explicitly correlated Gaussian lobe functions. Finite nuclear mass and scalar relativistic corrections are taken into account. This study contributes to the problem of the energy differences between doublet and quartet states of boron, which have not been measured to date. It is found that the ${}^2{P}_u\to {}^4{P}_g$ excitation energy, recommended in the Atomic Spectra Database, appears underestimated by more than 300 ${\mathrm{cm}}^{-1}$.

Different quantum phases of a hard-core boson induced by dipole-dipole interaction with varying angles of polarization are discussed in this work. We consider the two most influential leading terms with anisotropy due to the tilted polarization of the on-site boson in the square lattice. To ensure the concreteness of this truncation, we compare our phase diagrams, obtained numerically from the cluster mean-field theory (CMFT) and infinite projected entangled-pair state (iPEPS), with that of the long-range interacting model from quantum Monte Carlo. Next, we focus on the case where the azimuthal angle is fixed to $\varphi =\pi /4$. Using the mean-field analysis where the quantum spin operators are replaced by $c$ numbers, we aim to search for the underlying phases, especially the supersolid. Our results show a competing scenario mainly between two ordered phases with different sizes of unit cell, where a first-order transition takes place in between them. With the help of the CMFT and variational iPEPS, the phase boundaries predicted by the mean-field theory are determined more precisely. Our discoveries elucidate the possible underlying supersolid phases which might be seen in the ultracold experiments with strongly dipolar atoms. Moreover, our results indicate that an effective triangular optical lattice can be realized by fine tuning the polarization of dipoles in a square lattice.

We present a number of solutions to the three-dimensional Gross–Pitaevskii equation describing atomic Bose-Einstein condensates. This model supports elaborate patterns, including excited states bearing vorticity. The coherent structures exhibit striking topological features, involving combinations of vortex rings and multiple, possibly bent vortex lines. Although unstable, many of them persist for long times in dynamical simulations. These solutions were identified by a state-of-the-art numerical technique called deflation, which is expected to be applicable to many problems from other areas of physics.

We analyze the role played by quantum fluctuations on a Raman spin-orbit-coupled system in the stripe phase under attractive interspin interactions. We show that beyond-mean-field effects stabilize the collapse predicted by mean-field theory for attractive enough interspin interactions and induce the emergence of two phases, a gas and a liquid, which also show spatial periodicity along a privileged direction. We show that the energetically favored phase is determined by the Raman coupling and the spin-dependent scattering lengths. We obtain the ground-state solution of the finite system by solving the extended Gross-Pitaevskii equation and find self-bound dropletlike solutions that feature internal structure through a striped pattern. We estimate the critical binding number of these droplets and show that their value is experimentally accessible. We report an approximate energy functional in order to ease the evaluation of the Lee-Huang-Yang correction in practical terms.

The resonance properties of a layer on the surface of a spherical microresonator are investigated using geometrical optics. The resonance condition for these shell-guided modes is formulated. Shell-guided modes are located in the layer and are bounded by the inner and outer surfaces of the layer. It is shown that the resonance condition depends—similarly to the case of a homogeneous resonator—on the difference of the phase propagation of a ray crossing the layer and the corresponding phase propagation along the associated caustic. It is shown that the layer can support resonances only in a certain thickness range that depends, among other factors, on the resonance order and the wave number. A straightforward explanation is given for these limitations. Comparison with solutions from wave theory shows excellent agreement. A simple analytical solution is presented to calculate the sensitivity of the resonator to the refractive index and the thickness of the layer as well as to the refractive index of the environment.

Noninvasive and noncontact approaches of trapping nanoscale biospecimens have gained extensive interest due to their biological and nanotechnological applications. Here, we have proposed a tunable plasmonic nanotweezers that works in the terahertz region, and numerically demonstrated that a deep trapping potential well for a nanoscale dielectric nanoparticle can be generated through confining and enhancing the submillimeter-scale terahertz waves into a nanogap of graphene coaxial apertures. In addition, we further show the THz plasmonic nanotweezers is capable of stable trapping a 20-nm particle with a refractive index of 1.5 while the incident waves intensity is as low as $3.5\mathrm{mW}/\mu {\mathrm{m}}^2$ and the photon energy is below 20 meV. It is expected that the proposed THz nanotweezers could trap and manipulate nanoscale living biospecimens via a noninvasive approach.

The time-frequency degree of freedom of the electromagnetic field is the final frontier for single-photon measurements. The temporal and spectral distribution a measurement retrodicts (that is, the state it projects onto) is determined by the detector's intrinsic resonance structure. In this paper, we construct ideal and more realistic positive operator-valued measures (POVMs) that project onto arbitrary single-photon wave packets with high efficiency and low noise. We discuss applications to super-resolved measurements and quantum communication. In doing so we will give a fully quantum description of the entire photodetection process, give prescriptions for (in principle) performing single-shot Heisenberg-limited time-frequency measurements of single photons, and discuss fundamental limits and trade-offs inherent to single-photon detection.

Steerability is a characteristic of quantum correlations lying between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring the security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three-qubit state can violate the three-setting CJWR linear steering inequality, contrary to the two-setting linear steering inequality. This result explains that quantum steering correlations have limited shareability properties apart from the conventional 'nonshareable' monogamy constraint. In contrast to the two-measurement-setting scenario, the three-setting scenario turns out to be more useful for developing a deeper understanding of the shareability of tripartite steering correlations. Apart from the distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states, and genuine tripartite entanglement are presented here. The results enable the detection of different kinds of tripartite entanglement.

By developing a semiclassical analysis based on the eigenstate thermalization hypothesis, we determine the long time behavior of a large spin evolving with a nonlinear Hamiltonian. Despite integrable classical dynamics, we find the eigenstate thermalization hypothesis for the diagonal matrix elements of observables is satisfied in the majority of eigenstates, and thermalization of long time averaged observables is generic. The exception is an unusual mechanism for the breakdown of thermalization based on an unstable fixed point in the classical dynamics. Using the semiclassical analysis, we derive how the equilibrium values of observables encode properties of the initial state. This analysis shows an unusual memory effect in which the remembered initial state property is not conserved in the integrable classical dynamics. We conclude with a discussion of relevant experiments and the potential generality of this mechanism for long time memory and the breakdown of thermalization.

We obtain the general formula for the optimal rate on one of the subsystems that can be distilled from any bipartite quantum state by one-way local quantum-incoherent operations and classical communication. We provide lower and upper bounds on the assisted distillation of coherence using so-called one-shot entropies, and we establish a hierarchy of information quantities that can be used to calculate an assisted distillable rate in the asymptotical limit. We show that they asymptotically coincide with the quantum-incoherent relative entropy, and our findings imply a novel operational interpretation of quantum-incoherent relative entropy.

We consider the problem of separability of quantum channels via the Choi matrix representation given by the Choi-Jamiołkowski isomorphism. We explore three classes of separability across different cuts between systems and ancillae, and we provide a solution based on the mapping of the coordinates of the Choi state (in a fixed basis) to a truncated moment sequence (tms) $y$. This results in an algorithm which gives a separability certificate using semidefinite programming. The computational complexity and the performance of it depend on the number of variables $n$ in the tms and on the size of the moment matrix $M_t\left(y\right)$ of order $t$. We exploit the algorithm to numerically investigate separability of families of two-qubit and single-qutrit channels; in the latter case we can provide an answer for examples explored earlier through the criterion based on the negativity $N$, a criterion which remains inconclusive for Choi matrices with $N=0$.

A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for a dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing the density matrix. Specifically, the proper dynamical update rules are presented for the stochastic costate variables introduced by Pontryagin's maximum principle, and restrictions on the form of the terminal cost function are discussed. The proposed procedure is confirmed by comparing the results to those obtained from optimal control on Lindbladian dynamics. Numerically, the proposed formalism becomes time and memory efficient for large systems, and it can be generalized to describe non-Markovian dynamics.

The features of topological physics can manifest in a variety of physical systems in distinct ways. Periodically driven systems, with the advantage of high flexibility and controllability, provide a versatile platform to simulate many topological phenomena and may lead to novel phenomena that cannot be observed in the absence of driving. Here we investigate the influence of realistic experimental noise on the realization of a two-level system under a two-frequency drive that induces topologically nontrivial band structure in the two-dimensional Floquet space. We propose a dynamical decoupling scheme that sustains the topological phase transition overcoming the influence of dephasing. Therefore, the proposal would facilitate the observation of topological frequency conversion in the solid-state spin system, e.g., nitrogen-vacancy center in diamond.