In this study we employ a feed-forward artificial neural network (FFNN) architecture to perform the tomography of quantum states and processes obtained from noisy experimental data. To evaluate the performance of the FFNN, we use a heavily reduced data set and show that the density and process matrices of unknown quantum states and processes can be reconstructed with high fidelity. We use the FFNN model to tomograph 100 two-qubit and 128 three-qubit states which were experimentally generated on a nuclear magnetic resonance (NMR) quantum processor. The FFNN model is further used to characterize different quantum processes including two-qubit entangling gates, a shaped pulsed field gradient, intrinsic decoherence processes present in an NMR system, and various two-qubit noise channels (correlated bit flip, correlated phase flip, and a combined bit and phase flip). The results obtained via the FFNN model are compared with standard quantum state and process tomography methods and the computed fidelities demonstrates that, for all cases, the FFNN model outperforms the standard methods for tomography.

We explore a supervised machine-learning approach to estimate the entanglement entropy of multiqubit systems from few experimental samples. We put a particular focus on estimating both aleatoric and epistemic uncertainty of the network's estimate and benchmark against the best-known conventional estimation algorithms. For states that are contained in the training distribution, we observe convergence in a regime of sample sizes in which the baseline method fails to give correct estimates, while extrapolation only seems possible for regions close to the training regime. As a further application of our method, highly relevant for quantum simulation experiments, we estimate the quantum mutual information for nonunitary evolution by training our model on different noise strengths.

We propose a theoretical scheme of using two fixed-frequency resonator couplers to tune the interaction between two Xmon qubits. The indirect interaction between two qubits induced by two resonators can cancel each other, so direct qubit-qubit coupling is not essential for the switching off. So, we can suppress the static ZZ coupling with the weak direct qubit-qubit coupling and even eliminate the static ZZ coupling through the destructive interferences of the double-path couplers. The cross-Kerr resonance can induce additional poles for the static ZZ coupling which should be kept away during the two-qubit gates. The double-resonator couplers scheme could unfreeze some restrictions during the design of superconducting quantum chips and mitigate the static ZZ coupling, which might supply a promising platform for future superconducting quantum chips.

In the near future of the noisy intermediate-scale quantum (NISQ) era, almost all quantum computing devices will be restricted to a specific fixed qubits connectivity architecture. Thus, the synthesis of quantum circuits with limited connectivity is urgent. We design quantum circuit synthesis algorithms for basic and essential synthesis problems, such as quantum state preparation, general unitary synthesis, and quantum isometries. For any architecture, the controlled not (cnot) count is at most 5/3 times the state-of-the-art result on complete-graph architecture. For some specific architectures, such as square-grid ones, the ratio is reduced to 1.126. The numerical simulation result is confirmatory of theoretical conclusions. Our algorithms significantly reduce by more than $50\%$ additional cnot count compared to mapping algorithms. These algorithms help to implement the larger-scale algorithm in the physics device. Our results illustrate that well-designed synthesis algorithms can mitigate the problem of limited qubit connectivity in the NISQ era and may suggest the design of large-scale quantum devices.

We show that three-dimensional spherical-shell condensates respond to rotation by forming two aligned triangular Abrikosov-like vortex lattices on each hemispherical surface. The centrifugal force due to rotation causes an elliptical deformation of the spherical shell condensate shape and for faster rotation rates, drives the formation of a central multicharged vortex-antivortex pair at the poles surrounded by a ring of singly charged vortices in the bulk density. The vortex distributions observed in each hemisphere take a similar form to those found in rotating harmonic plus quartic traps.

A physical artificial complex-valued neuron is formed by four-wave mixing in a homogeneous three-dimensional Bose-Einstein condensate. Bragg beam-splitter pulses prepare superpositions of three plane-wave states as an input and the fourth wave as an output signal. The nonlinear dynamics of the nondegenerate four-wave mixing process leads to Josephson-like oscillations within the closed four-dimensional subspace and defines the activation function of a neuron. Due to the high number of symmetries, closed-form solutions can be found by quadrature and agree with the numerical simulation. The ideal behavior of an isolated four-wave mixing setup is compared to a situation with additional population of rogue states. We observe a robust persistence of the main oscillation. As an application for neural learning of this physical system, we train it on the xor problem. After 100 training epochs, the neuron responds to input data correctly at the ${10}^{-5}$ error level.

The statistical properties of speckle patterns have important applications in optics, oceanography, and transport phenomena in disordered systems. Here we obtain closed-form analytic results for the amplitude distribution of speckle patterns formed by a random number of partial waves characterized by an arbitrary phase distribution, generalizing classical results of the random-walk theory of speckle patterns. We show that the functional form of the amplitude distribution is solely determined by the distribution of the number of scatterers, while the phase distribution only influences the scale parameters. In the case of a nonrandom number of scatterers, we find an analytic expression for the amplitude distribution that extends the Rayleigh law to nonuniform random phases. For a negative binomial distribution of the number of scatterers, our results reveal that large fluctuations of the wave amplitudes become more pronounced in the case of biased random phases. We present numerical results that fully support our analytic findings.

We investigate theoretically optomechanically induced transparency in a whispering-gallery-mode microresonator coupled with three nanoparticles. We find that the presence of the third nanoparticle makes the transmission rate more sensitive in the vicinities of exceptional points (EPs). In addition, we also find that adjusting the relative position of the nanoparticles so that the system is near or far from the EPs can realize the switching of the probe light between slow and fast light. Our finding not only provides an alternative way to tune the spread of light but also can identify the existence of the third particle by detecting the change in the output spectrum of light so as to achieve particle detection. Our work may have potential application value in optical signal processing and communication.

We compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a Gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an Ansatz for the wave function and use machine learning techniques to variationally minimize the energy of systems from two to six particles. We provide extensive benchmarks for this toy model with other many-body methods, including exact diagonalization and the Hartree-Fock approximation. The neural quantum state provides the best energies across a wide range of interaction strengths. We find very different ground states depending on the sign of the interaction. In the nonperturbative repulsive regime, the system asymptotically reaches crystalline order. In contrast, the strongly attractive regime shows signs of bosonization. The neural quantum state continuously learns these different phases with an almost constant number of parameters and a very modest increase in computational time with the number of particles.

We evaluated the accuracy limit for estimating gravitational potential using optical lattice clocks by utilizing the quantum Cramér-Rao bound. We then compared the results for single-layer and multilayer optical lattice clocks. The results indicate that the lower bound of variance of the estimator of gravitational potential using finite-size optical lattice clocks diverges and recovers repeatedly as a function of time. Namely, the accuracy of the gravitational potential estimation is not a monotonic function of time owing to the effect of gravitational dephasing in finite-size optical lattice clocks. Further, this effect creates an estimation accuracy limit when attempting to avoid the divergence of the lower bound. When the number of layers in the optical lattice clock is sufficiently large, the limit is independent of the optical lattice clock details. The time required to reach this limit is calculated to be approximately 33 h for a three-dimensional optical lattice clock consisting of one million cadmium atoms due to Earth's gravity, and approximately the same for other atoms. This time is much longer than the current coherence time of $26\mathrm{s}$.

In this work the dressed-molecule theory is used to describe the two-dimensional quantum anomaly of breathing mode in a recent experimental system [M. Holten et al., Phys. Rev. Lett. 121, 120401 (2018); T. Peppler et al., Phys. Rev. Lett. 121, 120402 (2018)]. With the aid of a beyond-mean-field Gaussian pair fluctuation theory, we employ the dressed-molecule states to characterize the axial excited states and the Feshbach molecular states and propose a low-energy effective theory. We show that, in the whole crossover from a BCS superfluid to a Bose-Einstein condensate, our theory can describe the two-dimensional experimental systems precisely in the low-energy region. We explain the puzzling experimental observations of the smaller than expected breathing-mode frequency. Our establishment of the dressed-molecule theory for two-dimensional fermions can help in the understanding of the conformal anomaly in quasi-low-dimensional quantum systems.

We study the quantum walk of two interacting bosons on a two-leg ladder lattice in the presence of an artificial magnetic field. By considering a uniform flux piercing through the ladder, we show that in the limit of strong on-site repulsion and dominant rung hopping, an initially slow dynamics becomes fast, then slow and fast again with increase in the flux strength, indicating a re-entrant dynamics. This unusual behavior is found to be associated with the formation, breaking, and reformation of a bound pair state along the rung of the ladder. In addition to this we also find a reentrant behavior in the chiral dynamics where the chirality in the system first increases and then decreases with increase in interaction. We establish this unusual reentrant behavior in the dynamics by analyzing the radial velocity, spreading of correlation, center-of-mass shearing, and energy band diagrams.

We study the dynamics of a magneto-optical trap (MOT) operating at high bandwidth. We find the absolute importance of high recapture efficiency between cycles to maintain a practical atom number. We develop a simple one-dimensional model accounting for MOT trapping forces and pressure-induced collisions and verify with experimental data using ${}^{87}\mathrm{Rb}$. This is then applied to quantum sensing, predicting a shot noise limited sensitivity of $1\times {10}^{-7}\frac{\mathrm{g}}{\sqrt{\mathrm{Hz}}}$ for a gravimeter at 100 Hz operation. The results are useful for understanding MOT operation at high bandwidth, particularly in the context of developing mobile high-bandwidth quantum inertial sensors targeting dynamic environments and navigation applications.

Hilbert space fragmentation (HSF) is a phenomenon wherein the Hilbert space of an isolated quantum system splits into exponentially many disconnected subsectors. The fragmented systems do not thermalize after long-time evolution because the dynamics are restricted to a small subsector. Inspired by recent developments of the HSF, we construct the Hamiltonian that exhibits the HSF in momentum space. We show that persistent-current (PC) states emerge due to the HSF in the momentum space. We also investigate the stability of the PC states against the random potential, which breaks the structure of the HSF, and find that the decay rate of the PC is almost independent of the current velocity.

We investigate both analytically and numerically the dynamics of Rydberg-dressed Bose-Einstein condensates subjected to periodic modulation of the nonlocal repulsive interactions in time through temporally modulated control laser field. We show that, by utilizing such a control laser field, the nonlocal nonlinear interactions may be tuned actively, and hence a plane-wave state of matter wave can undergo a roton instability (RI) and Faraday instability (FI) simultaneously or separately, depending on the choice of the system parameters. Specifically, based on Floquet stability analysis, we find the evolution of small perturbations of the background allows the instability growth, thereby identifying instability regions with respect to density waves. Furthermore, we find that among other modes of the system the roton mode is most effectively excited due to a significant contribution of subharmonics of the excitation frequency. From the direct numerical simulations of nonlocal Gross-Pitaevskii equation (GPE) and the Fourier analysis on profile of the density waves, we further show the frequency of temporal oscillations of density waves coincides with half of the driving frequency, which, therefore, is the evidence of the parametric resonance and is characteristic of Faraday waves. In addition, an interesting possibility would be to generate a steady stand-wave in the condensate which can persist after the creation even though canceling the modulation, and finally the two-dimensional Faraday waves are excited through manipulating local or nonlocal nonlinear coefficients in the system.

We analyze the anisotropic Dicke model in the presence of a periodic drive and under a quasiperiodic drive. The study of drive-induced phenomena in this experimentally accessible model is important since, although it is simpler than full-fledged many-body quantum systems, it is still rich enough to exhibit many interesting features. We show that under a quasiperiodic Fibonacci (Thue-Morse) drive, the system features a prethermal plateau that increases as an exponential (stretched exponential) with the driving frequency before heating to an infinite-temperature state. In contrast, when the model is periodically driven, the dynamics reaches a plateau that is not followed by heating. In either case, the plateau value depends on the energy of the initial state and on the parameters of the undriven Hamiltonian. Surprisingly, this value does not always approach the infinite-temperature state monotonically as the frequency of the periodic drive decreases. We also show how the drive modifies the quantum critical point and discuss open questions associated with the analysis of level statistics at intermediate frequencies.

We show that, contrary to the claim by Kumar [Phys. Rev. A 96, 012332 (2017)], the quantum dual total correlation of an $n$-partite quantum state cannot be represented as the quantum relative entropy between $n-1$ copies of the quantum state and the product of $n$ different reduced quantum states for $n\ge 3$. Specifically, we argue that the latter fails to yield a finite value for generalized $n$-partite Greenberger-Horne-Zeilinger states.

We reaffirm the claim of Lee et al. [preceding Comment, Phys. Rev. A 108, 066401 (2023)] that the expression of quantum dual total correlation of a multipartite system in terms of quantum relative entropy as proposed in previous work [A. Kumar, Phys. Rev. A 96, 012332 (2017)] is not correct.

We consider a two-level system with a fixed energy spacing (detuning) between the two levels and a single transverse control field which can take values between zero and a maximum amplitude. Using Pontryagin's maximum principle, we completely solve the problem of generating in minimum time a uniform superposition of the two quantum states when starting from one of them, for all the values of the ratio between the maximum control amplitude and the detuning. For each value of this ratio we find the optimal pulse sequence to have the bang-bang form and calculate the durations of the pulses composing it. The suggested framework is not only restricted to the problem at hand, but it can be also exploited in the problem of fast charging a quantum battery based on a two-level system, as well as for the optimization of pulse sequences used for the controlled preparation of the excited state in a quantum emitter, which is a prerequisite for its usage as a single-photon source.