We have developed a Monte Carlo algorithm to explore the equilibrium and out-of-equilibrium properties of the Lieb-Liniger model. This Monte Carlo Bethe-ansatz (MCBA) algorithm has enabled us to successfully reconstruct statistical ensembles for equilibrium or postquench dynamics, thereby facilitating the calculation of macroscopic quantities of integrable models. Our results substantiate the validity of the (quench) thermodynamic Bethe-ansatz equation from the perspective of first-principles statistical physics. Additionally, we have employed this method to study the generalized Gibbs ensemble in relation to the postquench dynamics of the Lieb-Liniger model. Furthermore, we have demonstrated the MCBA algorithm's capacity to calculate correlations using Bethe-ansatz wave functions. Our approach offers an efficient methodology for the investigation of the equilibrium and out-of-equilibrium properties of integrable systems.

An approach to modeling the dynamics of x-ray amplified spontaneous emission and superfluorescence, the phenomenon of collective x-ray emission initiated by intense pulses of x-ray free-electron lasers, is developed based on stochastic partial differential equations. The equations are derived from first principles, and the relevant approximations, derivation steps, and extensions specific to stimulated x-ray emission are presented. The resulting equations take the form of three-dimensional generalized Maxwell-Bloch equations augmented with noise terms for both field and atomic variables. The derived noise terms possess specific correlation properties that enable the correct reconstruction of spontaneous emission. Consequently, the developed theoretical formalism is universally suitable for describing all stages of stimulated x-ray emission: spontaneous emission, amplified spontaneous emission, and superfluorescence. We present numerical examples that illustrate various properties of the emitted field, including spatiotemporal coherence and spectral-angular and polarization characteristics. We anticipate that the proposed theoretical framework will establish a robust foundation for interpreting measurements in stimulated x-ray emission spectroscopy, modeling x-ray laser oscillators, and describing other experiments leveraging x-ray superfluorescence.

Parton showers, which can efficiently incorporate quantum interference effects, have been shown to be run efficiently on quantum computers. However, so far these quantum parton showers have not included the full kinematical information required to reconstruct an event, which in classical parton showers requires the use of a veto algorithm. In this work, we show that adding one extra assumption about the discretization of the evolution variable allows one to construct a quantum veto algorithm, which reproduces the full quantum interference in the event, and allows one to include kinematical effects. We finally show that for certain initial states the quantum interference effects generated in this veto algorithm are classically tractable, such that an efficient classical algorithm can be devised.

Spin qubits in semiconductor structures bring the promise of large-scale two-dimensional integration, with the possibility to incorporate the control electronics on the same chip. In order to perform error correction on this platform, the characteristic features of spin qubits need to be accounted for. For example, qubit readout involves an additional qubit which necessitates careful reconsideration of the qubit layout. The noise affecting spin qubits has further peculiarities such as the strong bias towards dephasing. In this work we consider state-of-the-art error correction codes that require only nearest-neighbor connectivity and are amenable to fast decoding via minimum-weight perfect matching. Compared to the surface code, the XZZX code, the reduced-connectivity surface code, the ${\text{XYZ}}^2$ matching code, and the Floquet code all bring different advantages in terms of error threshold, connectivity, or logical qubit encoding. We present the spin-qubit layout required for each of these error correction codes, accounting for reference qubits required for spin readout. The performance of these codes is studied under circuit-level noise accounting for distinct error rates for gates, readout, and qubit decoherence during idling stages.

We exploit controlled breaking of time-reversal symmetry to realize coherent routing of quantum information in spin networks. The key component of our scheme is a spin triangle whose chirality is determined by the quantum state of a control qubit which thus defines the propagation direction, or a superposition thereof, of the quantum information. We then consider a particular realization of a coherent router using Rydberg atoms. Our results can facilitate scalable quantum information processing and communication in large arrays of Rydberg atoms.

A quantum autoencoder is a quantum neural network model for compressing information stored in quantum states. However, one needs to process information stored in quantum circuits for many tasks in the emerging quantum information technology. In this work, generalizing the ideas of classical and quantum autoencoders, we introduce the quantum circuit autoencoder (QCAE) model to compress and encode information within quantum circuits. We provide a comprehensive protocol for QCAE and design a variational quantum algorithm, varQCAE, for its implementation. We theoretically analyze this model by deriving conditions for lossless compression and establishing both upper and lower bounds on its recovery fidelity. Finally, we apply varQCAE to three practical tasks, and numerical results show that it can effectively (1) compress the information within quantum circuits, (2) detect anomalies in quantum circuits, and (3) mitigate the depolarizing noise in quantum circuits. These suggest that our algorithm is potentially applicable to other information processing tasks for quantum circuits.

Explaining the behavior of macroscopic objects from the point of view of the quantum paradigm has challenged the scientific community for the past century. A mechanism of gravitational self-interaction, governed by the so-called Schrödinger-Newton equation, is among the proposals that aim to shed some light on it. Despite all efforts, this mechanism has been proven difficult to probe. Here, we consider a Stern-Gerlach-like experiment to try it out. The Schrödinger-Newton equation can be analytically solved under certain proper conditions, and a change-of-phase effect induced by the gravitational self-interacting potential can be calculated.

We consider quantum systems with a Hamiltonian containing a weak perturbation, i.e., $\mathit{H}={\mathit{H}}_{\mathit{0}}+\mathit{\lambda }·\tilde{\mathit{H}}, \mathit{\lambda }=\{{\lambda }_1,{\lambda }_2,...,\}, \tilde{\mathit{H}} =\{H_1,H_2,...,\}, \left|\mathit{\lambda }\right|\ll 1$, and address situations where $\tilde{\mathit{H}}$ is known but the values of the couplings $\mathit{\lambda }$ are unknown and should be determined by performing measurements on the system. We consider two scenarios: in the first one we assume that measurements are performed on a given stationary state of the system, e.g., the ground state, whereas in the second one an initial state is prepared and then measured after evolution. In both cases, we look for the optimal measurements to estimate the couplings and evaluate the ultimate limits to precision. In particular, we derive general results for one and two couplings and analyze in detail some specific qubit models. Our results indicate that dynamical estimation schemes may provide enhanced precision upon a suitable choice of the initial preparation and the interaction time.

We investigate the topological edge transmission of excitation based on the one-dimensional Su-Schrieffer-Heeger lattice with purely imaginary on-site potential and nonreciprocal nearest-neighbor hopping. We find that, when the system has only the nonreciprocal intracell hopping, the topological excitation transmission can be implemented only when the localization direction of the non-Hermitian skin effect matches the localization direction of edge state. When the lattice has the purely imaginary on-site potential and nonreciprocal intracell hopping, we demonstrate that the positive purely imaginary potential is the dominant effect of implementing the topological excitation transmission compared with the non-Hermitian skin effect. Furthermore, we also investigate the joint effect between the purely imaginary on-site potential and nonreciprocal intercell hopping, which reveals that the non-Hermitian skin effect induced via the large nonreciprocal parameter determines the successful topological excitation transmission. Our investigations show the different influences of two kinds of non-Hermitian effects on the topological excitation transmission, which may promote the implementation of topological transmission in the practical open quantum system.

In optimization, a pivotal challenge involves minimizing or maximizing polynomial functions, which is often tackled through iterative methods. Although quantum algorithms hold promise to enhance these techniques, a practical quantum protocol is still elusive. In this paper, first, we utilize the linear combination of unitaries framework for gradient-based optimization of an arbitrary polynomial, where the entire optimization process can be represented as cascaded circuits. One standout feature of this protocol is its explicit implementation circuit, which has the ability to circumvent the necessity for a quantum random access memory structure. Then the feasibility of this protocol is initially assessed through numerical simulation, exploring its robustness in several noise scenarios. Finally, the paper explores the associated computational cost, sample, architecture, and time costs, and compares them with those of existing methods. Notably, the proposed protocol shows significant efficiency gains in terms of architecture cost. If certain conditions are met, both sample and time costs can be significantly reduced, addressing a critical weakness in previous works.

We analyze the dynamics of two-qubit entangled Bell states in coupled quantum dots (QDs) in the presence of both fluctuations and coherent electron hopping between the dots. The explicit expression for time-dependent probability to find the system in the different Bell states was obtained for various initial conditions by means of Keldysh diagram technique. It was revealed that time evolution of one pair of Bell states and its decay rate strongly differs from another one. It was demonstrated that one pair of Bell states is more robust against fluctuations than another one. The stationary occupation of Bell states for different initial conditions was also analyzed. Obtained results are important for the problems where long-living Bell states are needed such as the security of quantum communication and quantum information processing.

Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy measures. Here we propose a variational quantum algorithm for estimating the von Neumann and Rényi entropies, as well as the measured relative entropy and measured Rényi relative entropy. Our approach first parametrizes a variational formula for the measure of interest by a quantum circuit and a classical neural network and then optimizes the resulting objective over parameter space. Numerical simulations of our quantum algorithm are provided, using a noiseless quantum simulator. The algorithm provides accurate estimates of the various entropy measures for the examples tested, which renders it a promising approach for usage in downstream tasks.

Scalable quantum computers hold the promise to solve hard computational problems, such as prime factorization, combinatorial optimization, simulation of many-body physics, and quantum chemistry. While being key to understanding many real-world phenomena, simulation of nonconservative quantum dynamics presents a challenge for unitary quantum computation. In this work, we focus on simulating nonunitary parity-time-symmetric systems, which exhibit a distinctive symmetry-breaking phase transition as well as other unique features that have no counterpart in closed systems. We show that a qutrit, a three-level quantum system, is capable of realizing this nonequilibrium phase transition. By using two physical platforms, an array of trapped ions and a superconducting transmon, and by controlling their three energy levels in a digital manner, we experimentally simulate the parity-time-symmetry-breaking phase transition. Our results indicate the potential advantage of multilevel (qudit) processors in simulating physical effects, where additional accessible levels can play the role of a controlled environment.

Using a dissipative quantum neural network (DQNN) accompanied by conjugate layers, we upgrade the performance of the existing quantum autoencoder (QAE) network as a quantum denoiser of a noisy $m$-qubit GHZ state. Our denoising architecture requires a much smaller number of learning parameters, which can decrease the training time, especially when a deep or stacked DQNN is needed to approach the highest fidelity in the noisy intermediate-scale quantum era. In QAE, we reduce the connection between the hidden layer's qubits and the output's qubits to modify the decoder. The Renyi entropy of the hidden and output qubits' states is analyzed with respect to other qubits during learning iterations. During the learning process, if the hidden layer remains connected to the input layers, the network can almost perfectly denoise unseen noisy data with a different underlying noise distribution using the learning parameters acquired from training data.

Classical and quantum communication protocols share similarities in terms of signal modulation, transmission, and reception, providing a basis for their integration. The integration of these protocols can lead to high-efficiency and low-cost performance by utilizing a single set of communication infrastructures to simultaneously achieve continuous-variable quantum key distribution and classical communication on a single wavelength. In this paper, we propose a simultaneous quantum and classical communication (SQCC) protocol based on multiparameter modulation, which combines pulse position modulation (PPM) for classical communication and Gaussian-distributed modulation (GM) for quantum key distribution, named GMCS-PPM-SQCC protocol. Classical information is transmitted using the arrival time parameter of the coherent state, while quantum key information is distributed through the two quadrature components of the coherent state. Coherent detection is used to detect all three parameters, and different data processing schemes are utilized to extract the corresponding information. We verified the feasibility of the protocol through simulations, discussed its secure transmission distance, bit error rate, and secret key rate in realistic scenarios. Our protocol has better phase noise tolerance than traditional SQCC protocol. It can further facilitates the integration of classical and quantum communication, and contributes to the deployment and application of QKD.

We report on the combined experimental and theoretical studies of the single-electron capture collisions of ${\mathrm{Ar}}^{8+}$ projectiles with the ${\mathrm{H}}_2$ molecules at 1, 2, and 4 keV/u collision energies. The nondissociative recoil ${\mathrm{H}}_2{}^{+}$ molecular ions are measured in coincidence with the charge-changing ${\mathrm{Ar}}^{7+}$ projectiles. The relative cross sections of the different state-selective capture channels are obtained from the experimentally measured $Q$-value spectra. The $1s$ electron transfers to the highly excited $4d+4f, 5s, 5p, 5d+5f+5g, 6s+6p$, and $6d+6f+6g+6h$ states are resolved experimentally. The differential scattering angle distributions for the dominant $1s$ to $5s, 5p$, and $5d+5f+5g$ transitions are compared with the two-center atomic orbital close-coupling methods. A collision energy-dependent dynamical coupling effect is also observed for the $1s\to 5p_0$ and $1s\to 5p_{\pm 1}$ transitions. The dominant oscillatory structures in the scattering-angle distributions are attributed to Stueckelberg-type oscillations. In contrast, the less visible undulations in the smaller scattering angles imprint the signature of the quantum matter-wave scattering of the projectiles. The quantum nature of the oscillations in the angular distributions is further validated by classical calculations. Our study thus illustrates the highly excited quantum state-selective electron capture process and sheds light on the scattering-angle-range-dependent collision dynamics for highly charged ion-molecule collisions in the highly perturbative regime.

Positronium hydride $\left(\text{PsH}\right)$ is a weakly bound (molecular) state of two electrons $\left(e^{-}\right)$, a positron $\left(e^{+}\right)$, and a proton $\left(p^{+}\right)$. Due to the $e^{-}-e^{+}$ annihilation, it decays to a number of processes, where the radiationless decay is one of the most important channels. In this decay process, the photons released from the $e^{-}-e^{+}$ annihilation are absorbed by the remaining $e^{-}$ and $p^{+}$ in PsH, giving us $\text{PsH}\to e^{-}{p}^{+}$. For a particular spin (singlet) configuration of the constituents of PsH, the radiationless decay rate of PsH was determined by Aslam et al. [Phys. Rev. A 104, 052803 (2021)]. In this work, we calculate the decay rate of $\text{PsH}\to e^{-}{p}^{+}$ by exercising all possible spin orientations of PsH and the final states $e^{-}$ and $p^{+}$. By summing all the contributions, we verify that the result is the same if we calculate it using the standard fermion spin-sum technique of quantum field theory.

Following the sudden single ionization of ${\text{CO}}_2$ in ultrashort extreme ultraviolet pump pulses, after exposure to delayed 780- or 400-nm probe-laser pulses, we propagate the coupled nuclear motion in ${{\text{CO}}_2}^{+}$ on the $A{}^2{\mathrm{\Pi }}_u$, $B{{}^2{\mathrm{\Sigma }}_u}^{+}$, $C{{}^2{\mathrm{\Sigma }}_g}^{+}$, $a{{}^4{\mathrm{\Sigma }}_g}^{-}$, and $b{}^4{\mathrm{\Pi }}_u$ potential-energy surfaces of the excited molecular cation, including all vibronic degrees of freedom. We calculate potential-energy surfaces, diabatic couplings, and probe-laser-induced dipole couplings ab initio and heuristically model spin-orbit couplings. Based on our numerical results, we scrutinize the relative importance of diabatic, dipole, and spin-orbit couplings during the dissociation of ${{\text{CO}}_2}^{+}$ into $\text{O}{(}^3{P}_g)+{\text{CO}}^{+}\left(X{}^2{\mathrm{\Sigma }}^{+}\right)$ and ${\text{O}}^{+}{(}^4{S}_u)+\text{CO}\left(X{}^1{\mathrm{\Sigma }}^{+}\right)$, provide rovibrational-excitation distributions of the ${\mathrm{CO}}^{+}$ fragments, and discuss pump-probe-delay-dependent kinetic-energy-release spectra. Addressing the nuclear dynamics near the conically intersecting $A{}^2{\mathrm{\Pi }}_u$ and $B{{}^2{\mathrm{\Sigma }}_u}^{+}$ states of ${{\text{CO}}_2}^{+}$, we reproduce the valence-hole oscillation period of 115 fs measured by Timmers et al. [Phys. Rev. Lett. 113, 113003 (2014)]. In addition, we predict and characterize, in terms of quantum beats between specific stationary vibronic states, a 3.1-ps fragment-yield oscillation.

We study the Fermi polaron problem with dipolar fermions in a bilayer geometry, where a single dipolar particle in one layer interacts with a Fermi sea of dipolar fermions in the other layer. By evaluating the polaron spectrum, we obtain the appearance of a series of attractive branches when the distance between the layers diminishes. We relate these to the appearance of a series of bound two-dipole states when the interlayer dipolar interaction strength increases. By inspecting the orbital angular-momentum component of the polaron branches, we observe an interchange of orbital character when system parameters such as the gas density or the interlayer distance are varied. Furthermore, we study the possibility that the lowest energy two-body bound state spontaneously acquires a finite center-of-mass momentum when the density of fermions exceeds a critical value, and we determine the dominating orbital angular momenta that characterize the pairing. Finally, we propose to use the tunneling rate from and into an auxiliary layer as an experimental probe of the impurity spectral function.