An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase-space methods such as the truncated Wigner approximation (TWA) have the advantage of being easily scalable and applicable to arbitrary dimensions. In this work we adapt the TWA to generic spin-boson models by making use of recently developed algorithms for discrete phase spaces [J. Schachenmayer, A. Pikovski, and A. M. Rey, Phys. Rev. X 5, 011022 (2015)]. Furthermore we go beyond the standard TWA approximation by applying a scheme based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations to our coupled spin-boson model. This allows us, in principle, to study how systematically adding higher-order corrections improves the convergence of the method. To test various levels of approximation we study an exactly solvable spin-boson model, which is particularly relevant for trapped-ion arrays. Using TWA and its BBGKY extension we accurately reproduce the time evolution of a number of one- and two-point correlation functions in several dimensions and for an arbitrary number of bosonic modes.

We consider the dynamics of a disordered ensemble of qubits interacting with a single-mode photon field, which is described by an exactly solvable inhomogeneous Dicke model. In particular, we concentrate on the crossover from few-qubit systems to the system of many qubits and analyze how the collective behavior of a coupled qubit-cavity system emerges despite the broadening. We show that quantum interference effects survive in the mesoscopic regime—the dynamics of an entangled Bell state encoded into the qubit subsystem remains highly sensitive to the symmetry of the total wave function. Moreover, relaxation of these states is slowed down due to the formation of collective dark states weakly coupled to light. Dark states also significantly influence the dynamics of the excitations of a photon subsystem by absorbing them into the qubit subsystem and releasing quasiperiodically in time. We argue that the predicted phenomena can be useful in quantum technologies based on superconducting qubits. For instance, they provide tools to deeply probe both collective and quantum properties of such artificial macroscopic systems.

As the memory effect may be helpful in quantum information processing, non-Markovian dynamics plays an important role in the description of many-body open systems. Among these topics, the system consisting of independent qubits interacting with several coupled environments is of particular interest. In this paper, we study the exact non-Markovian dynamics of two independent qubits. Each of the qubits interacts individually with its environment, and these two environments coupled with each other. We investigate the non-Markovianity measure of the system for the whole parameter regime without the rotating-wave approximation (RWA) and compare the results with that under the RWA. We find that the non-Markovianity measure for two qubits manifests a transition from a non-Markovian to Markovian regime regardless of the coupling strength between the environments. The physical origin of this transition is revealed, and a possible observation of the prediction in superconducting quantum interference devices is discussed.

We study a system of two coupled waveguides respectively carrying optical damping and optical gain in addition to squeezing elements in one or both waveguides. Such a system is expected to generate highly entangled light fields in the two waveguides. Especially, if the light fields are strong enough, a macroscopic, continuous-variable entanglement can be achieved. We, however, show that the degree of the created entanglement is significantly affected by the quantum noises associated with the amplification and dissipation. The entanglement for the different configurations of the setup is quantified to illustrate how the quantum noises limit such entanglement as well as determine its actual time evolution patterns. In contrast to its sensitivity to the quantum noises, the degree of entanglement is irrelevant to the input light intensities, given the inputs in coherent states.

The traditional approach to the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in open quantum systems (implicitly) assumes that the bath (environment) state returns to its original state after each instantaneous projective measurement on the system and thus ignores the cross-correlations of the bath operators between different Zeno intervals. However, this assumption is not generally true, especially for a bath with a considerably nonnegligible memory effect and for a system repeatedly projected into an initial general superposition state. We find that, in stark contrast to the result of a constant value found in the traditional approach, the scaled average decay rate in unit Zeno interval of the survival probability is generally time dependent or shows an oscillatory behavior. In the case of a strong bath correlation, the transition between the QZE and the QAZE depends sensitively on the number of measurements $N$. For a fixed $N$, a QZE region predicted by the traditional approach may in fact already be in the QAZE region. We illustrate our findings using an exactly solvable open qubit system model with a Lorentzian bath spectral density, which is directly related to realistic circuit cavity quantum electrodynamics systems. Thus the results and dynamics presented here can be verified with current superconducting circuit technology.

We propose a quantum algorithm for support matrix machines (SMMs) that efficiently addresses an image classification problem by introducing a least-squares reformulation. This algorithm consists of two core subroutines: a quantum matrix inversion (Harrow-Hassidim-Lloyd, HHL) algorithm and a quantum singular value thresholding (QSVT) algorithm. The two algorithms can be implemented on a universal quantum computer with complexity $O\left[log\left(npq\right)\right]$ and $O\left[log\left(pq\right)\right]$, respectively, where $n$ is the number of the training data and $pq$ is the size of the feature space. By iterating the algorithms, we can find the parameters for the SMM classfication model. Our analysis shows that both HHL and QSVT algorithms achieve an exponential increase of speed over their classical counterparts.

We investigate multipartite entanglement and a quantum phase transition for spin chain systems by making use of the density-matrix renormalization-group method in the form of matrix-product states. It is found that multipartite entanglement changes dramatically near the critical region and the residual-to-global entanglement ratio reaches its maximum at the critical point of the quantum phase transition. These results indicate that multipartite entanglement as well as the residual-to-global entanglement ratio can serve as good indicators to detect a quantum phase transition. We also demonstrate a linear relation between the next-nearest-neighbor interaction strength and the critical magnetic field for an $XYZ$ spin chain by using multipartite entanglement and quantum coherence.

The largest obstacle to perform quantum information processing is decoherence of a system. In order to overcome this, various techniques, such as dynamical decoupling and quantum Zeno effects, have been proposed and demonstrated. Here, we present an NMR model with which various decoherence suppression techniques can experimentally be evaluated. By changing the conditions in the sample preparation, we can engineer an environment to interact the system that contains the information. Moreover, we can efficiently describe the dynamics by the operator-sum representation due to the simplicity of our model. As concrete examples, we have investigated the performance of dynamical decoupling with several molecules. Our model provides a useful test bench to understand the mechanism of decoherence induced by a noisy environment and to examine various ideas of decoherence suppression techniques.

The set of pure spin states with vanishing spin expectation value can be regarded as the set of the less coherent pure spin states. This set can be divided into a finite number of nested subsets on the basis of higher order moments of the spin operators. This subdivision relies on the notion of anticoherent spin state to order $t$: A spin state is said to be anticoherent to order $t$ if the moment of order $k$ of the spin components along any directions are equal for $k=1,2,...,t$. Most spin states are neither coherent nor anticoherent, but can be arbitrary close to one or the other. In order to quantify the degree of anticoherence of pure spin states, we introduce the notion of anticoherence measures. By relying on the mapping between spin-$j$ states and symmetric states of $2j$ spin $1/2$ (Majorana representation), we present a systematic way of constructing anticoherence measures to any order. We briefly discuss their connection with measures of quantum coherence. Finally, we illustrate our measures on various spin states and use them to investigate the problem of the existence of anticoherent spin states with degenerated Majorana points.

We theoretically investigate the dynamical Casimir effect in a single-mode cavity endowed with a driven off-resonant mirror. We explore the dynamics of photon generation as a function of the ratio between the cavity mode and the mirror's driving frequency. Interestingly, we find that this ratio defines a threshold—which we referred to as a metal-insulator phase transition—between exponential growth and low photon production. The low photon production is due to Bloch-like oscillations that produce a strong localization of the initial vacuum state, thus preventing higher generation of photons. To break localization of the vacuum state and enhance the photon generation, we impose a dephasing mechanism, based on dynamic disorder, into the driving frequency of the mirror. Additionally, we explore the effects of finite temperature on the photon production. Concurrently, we propose a classical analog of the dynamical Casimir effect in engineered photonic lattices, where the propagation of classical light emulates the photon generation from the quantum vacuum of a single-mode tunable cavity.

We measure the hyperfine structure of the $5p^{6}5d{}^2{D}_{3/2}$, $5p^{6}5d{}^2{D}_{5/2}$, $5p^{6}4f{}^2{F}_{5/2}^o$, and $5p^{6}4f{}^2{F}_{7/2}^o$ levels in doubly ionized lanthanum (La iii; ${\mathrm{La}}^{2+}$) in a hollow-cathode lamp using optogalvanic spectroscopy. Analysis of the observed spectra allows us to determine the hyperfine $A$ coefficients for these levels to be $A_{D3/2}=412\left(4\right)$ MHz, $A_{D5/2}=20\left(5\right)$ MHz, $A_{F5/2}=319\left(2\right)$ MHz, and $A_{F7/2}=155\left(4\right)$ MHz, and provide estimates for the hyperfine $B$ coefficients as $B_{D3/2}=105\left(29\right)$ MHz, $B_{D5/2}=157\left(40\right)$ MHz, $B_{F5/2}=-2\left(53\right)$ MHz, and $B_{F7/2}=171\left(51\right)$ MHz.

We conduct a theoretical study of $\mathrm{SU}(N$) fermions confined by a one-dimensional harmonic potential. First, we introduce a numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the $\mathrm{SU}(N$) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz—derived for a Heisenberg SU(2) spin chain—is extendable to these $N$-component systems. Lastly, we consider balanced $\mathrm{SU}(N$) Fermi gases that have an equal number of particles in each spin state for $N=2,3,4$. In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of $N$-component fermions may be accurately inferred from the corresponding few-body systems of $N$ distinguishable particles.

The partition function, a fundamental tenet in statistical thermodynamics, contains in principle all thermodynamic information about a system. It encapsulates both microscopic information through the quantum energy levels and statistical information from the partitioning of the particles among the available energy levels. For identical particles, this statistical accounting is complicated by the symmetry requirements of the allowed quantum states. In particular, for Fermi systems, the enforcement of the Pauli principle is typically a numerically demanding task, responsible for much of the cost of the calculations. The interplay of these three elements—the structure of the many-body spectrum, the statistical partitioning of the $N$ particles among the available levels, and the enforcement of the Pauli principle—drives the behavior of mesoscopic and macroscopic Fermi systems. In this paper, we develop an approach for the determination of the partition function, a numerically difficult task, for systems of strongly interacting identical fermions and apply it to a model system of harmonically confined, harmonically interacting fermions. This approach uses a recently introduced many-body method that is an extension of the symmetry-invariant perturbation method (SPT) originally developed for bosons. It uses group theory and graphical techniques to avoid the heavy computational demands of conventional many-body methods which typically scale exponentially with the number of particles. The SPT application of the Pauli principle is trivial to implement since it is done “on paper” by imposing restrictions on the normal-mode quantum numbers at first order in the perturbation. The method is applied through first order and represents an extension of the SPT method to excited states. Our method of determining the partition function and various thermodynamic quantities is accurate and efficient and has the potential to yield interesting insight into the role played by the Pauli principle and the influence of large degeneracies on the emergence of the thermodynamic behavior of large-$N$ systems.

We propose a protocol for realizing the stripe phase in two spin models on a two-dimensional square lattice, which can be implemented with strongly magnetic atoms (Cr, Dy, Er, etc.) in optical lattices by encoding spin states into Zeeman sublevels of the ground-state manifold. The protocol is tested with cluster-mean-field time-dependent variational Ansätze, validated by comparison with exact results for small systems, which enable us to simulate the dynamics of systems with up to 64 sites during the state-preparation protocol. This allows us, in particular, to estimate the time required for preparation of the stripe phase with high fidelity under real experimental conditions.

In this paper, we consider the nonlinear response to the external electromagnetic field of a plasmonic nanolaser consisting of a metallic nanoparticle interacting with a pumped active medium. We investigate plasmonic nanolaser dynamics in the regime of loss compensation, when at certain values of the magnitude and frequency of the external electromagnetic field the energy is transmitted neither from the electromagnetic field to the plasmonic nanolaser nor from the plasmonic nanolaser to the electromagnetic field. We consider the influence of noise and show that in the regime of loss compensation the effect of stochastic resonance takes place. Noise is effectively suppressed and the time of phase correlation increases by an order of magnitude compared to other parameters of external electromagnetic field. We also demonstrate that the effective diffusion coefficient of the phase of the plasmonic nanolaser's response decreases by an order of magnitude, which reveals stochastic resonance as well.

We theoretically study the dynamics and resonance shift of the Rabi model with frequency modulation, i.e., the Rabi model driven additionally by a slow longitudinal field, by using the counterrotating-hybridized rotating-wave (CHRW) method, aiming to illustrate the effects of the counterrotating (CR) terms of the transverse field. The CHRW method is based on a unitary transformation and reduces the aperiodic Hamiltonian to an effective periodic Hamiltonian that can be efficiently treated by Floquet theory. The validity of the effective Hamiltonian and widely used rotating-wave approximation (RWA) Hamiltonian is carefully examined compared to the numerically exact results over a wide parameter range. It is found that the effective Hamiltonian gives a correct description, while the RWA breaks down in the strong driving regime. Interestingly, we show that under certain conditions the longitudinal field can be used to modify resonance widths such that resonance widths can be comparable to the magnitude of the Bloch-Siegert (BS) shift, which in turn makes the CR-induced BS shift significant and leads to the complete breakdown of the RWA even in a moderately strong driving regime (in which the RWA holds for the Rabi model without frequency modulation). In addition, by using the effective Hamiltonian, we can efficiently access resonance positions for the bichromatically driven qubit and study how the resonance shifts due to the combined effects of the CR terms and frequency modulation. For a weak longitudinal field, we show that resonance positions can be analytically calculated from the effective Rabi frequency for the effective Hamiltonian, which are in excellent agreement with the numerically exact results.

We propose a scheme to speed up adiabatic passage by using Lyapunov control theory. This is a good choice to solve the problem that may emerge in Berry's transitionless quantum driving [M. V. Berry, J. Phys. A 42, 365303 (2009)]. That is, the extra couplings in the counterdiabatic driving Hamiltonian can be avoided by choosing the available control Hamiltonian in an actual physical system. As examples, we shorten the evolution time of adiabatic population transfer in a three-level system and the entanglement generation in a cavity quantum electrodynamics system. Moreover, the occupation of an intermediate state can be sharply suppressed by properly choosing the control Hamiltonian in the three-level system. The scheme can also be generalized to a complex system where the exact expressions of adiabatic eigenstates are difficult to obtain.

We present a method for accelerating adiabatic protocols for systems involving a coupling to a continuum, one that cancels both nonadiabatic errors as well as errors due to dissipation. We focus on applications to a generic quantum state transfer problem, where the goal is to transfer a state between a single level or mode, and a propagating temporal mode in a waveguide or transmission line. Our approach enables perfect adiabatic transfer protocols in this setup, despite a finite protocol speed and a finite waveguide coupling. Our approach even works in highly constrained settings, where there is only a single time-dependent control field available.

We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithm development.

For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. The phase of these drives can be used to generate zero-duration arbitrary virtual $Z$ gates, which, combined with two $X_{\pi /2}$ gates, can generate any SU(2) gate. Here we show how to best utilize these virtual $Z$ gates to both improve algorithms and correct pulse errors. We perform randomized benchmarking using a Clifford set of Hadamard and $Z$ gates and show that the error per Clifford is reduced versus a set consisting of standard finite-duration $X$ and $Y$ gates. $Z$ gates can correct unitary rotation errors for weakly anharmonic qubits as an alternative to pulse-shaping techniques such as derivative removal by adiabatic gate (DRAG). We investigate leakage and show that a combination of DRAG pulse shaping to minimize leakage and $Z$ gates to correct rotation errors realizes a 13.3 ns $X_{\pi /2}$ gate characterized by low error $[1.95\left(3\right)\times {10}^{-4}]$ and low leakage $[3.1\left(6\right)\times {10}^{-6}]$. Ultimately leakage is limited by the finite temperature of the qubit, but this limit is two orders of magnitude smaller than pulse errors due to decoherence.