In this paper we investigate the application of optimal control of a single qubit coupled to an ohmic heat bath. For the weak bath coupling regime, we derive a Bloch-Redfield master equation describing the evolution of the qubit state parametrized by vectors in the Bloch sphere. By use of the optimal control methodology we determine the field that generates an arbitrary single qubit rotation in minimum time. In particular we develop an efficient method for solving the time-optimal control problem, namely the implementation of $X$ gate, which consists of a rotation about the $\overrightarrow{ox}$ axis through angle $\pi$. The time-optimal control problem requires a bounded control. If upper and lower bounds are imposed for the external control, the optimal solution is of bang-bang type and switches from the upper to the lower values of the control bounds. We compare our results using the techniques of automatic differentiation to compute the gradient for the cost functional with some known results using Pontryagin's minimum principle. We use an alternative numerical approach for the optimization strategy.

Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand us to accelerate the evolution so that the adiabatic errors can be prevented from accumulation. Here, by treating this trade-off task as a multiobjective optimization problem, we propose a gradient-free learning algorithm with pulse smoothing technique to search optimal adiabatic quantum pathways and apply it to the Landau-Zener Hamiltonian and Grover search Hamiltonian. Numerical comparisons with a linear schedule, local adiabatic theorem induced schedule, and gradient-based algorithm searched schedule reveal that the proposed method can achieve significant performance improvements in terms of the adiabatic time and the instantaneous ground-state population maintenance. The proposed method can be used to solve more complex and real adiabatic quantum computation problems.

Cryptographic protocols are often based on the two main resources: private randomness and private key. In this paper, we develop the relationship between these two resources. First, we show that any state containing perfect, directly accessible, private key (a private state) is a particular case of the state containing perfect, directly accessible, private randomness (an independent state). We then demonstrate a fundamental limitation on the possibility of transferring the privacy of random bits in quantum networks with an intermediate repeater station. More precisely, we provide an upper bound on the rate of repeated randomness in this scenario, similar to the one derived for private key repeaters. This bound holds for states with positive partial transposition. We further demonstrate the power of this upper bound by showing a gap between the localizable and the repeated private randomness for separable Werner states. In the case of restricted class of operations, we provide also a bound on repeated randomness which holds for arbitrary states.

We present optimal schemes, based on photon-number measurements, for Gaussian state tomography and for Gaussian process tomography. An $n$-mode Gaussian state is completely specified by $2n^2+3n$ parameters. Our scheme requires exactly $2n^2+3n$ distinct photon-number measurements to tomograph the state and is therefore optimal. Furthermore, we describe an optimal scheme to characterize Gaussian processes by using coherent-state probes and photon-number measurements. With much recent progress in photon-number-measurement experimental techniques, we hope that our scheme will be useful in various quantum information processing protocols including entanglement detection, quantum computation, quantum key distribution, and quantum teleportation. This work builds upon the work of Parthasarathy and Sengupta [Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18, 1550023 (2015)].

The second vibrational overtone transition, ${\nu }^{\prime },J^{\prime }=3,1\leftarrow \nu ,J=0,0$, in ${\text{OH}}^{-}$ confined in a 22-pole radio frequency ion trap has been measured using a laser induced reaction with molecular hydrogen. The resultant spectral line is found at 10 150.94(2) ${\mathrm{cm}}^{-1}$ and the excitation rate of this overtone excitation is obtained, which sensitively probes the molecular potential surface. The Doppler broadened line profile is used to determine the translational temperature of the ions in buffer gas temperatures ranging from 9(1) to 52(1) K. The translational temperatures closely follow those of the buffer gas over this range, including an offset caused by radio frequency heating. In comparison with previous measurements of the rotational temperatures of trapped ions, we show that translational and rotational temperatures do not equilibrate at the low buffer gas temperatures.

We report full quantum scattering cross sections for the peculiar ${}^{17}\mathrm{O}+{}^{17}\mathrm{O}{}^{17}\mathrm{O}$ system, at relatively low collision energies. We consider different types of collision-induced transitions, as the indistinguishability of the three nuclei allows for the mixing of reactive, inelastic, and elastic processes. Furthermore, due to the nonzero nuclear spin of ${}^{17}\mathrm{O}$ and the existence of nuclear spin isomers ortho- and para-${\mathrm{O}}_2$, we pay particular attention to transitions between these two species, that is, the ortho-para conversion process. We find that the corresponding cross section has a magnitude comparable to that of the ${\mathrm{H}}^{+}+{\mathrm{H}}_2$ counterpart.

A method combining an Ehrenfest-like approach, which minimizes the number of surface hops, with Tully's fewest switches surface hopping is proposed for the description of nonadiabatic molecular dynamics in the presence of an external electromagnetic field. When two states are strongly coupled by the applied light field, an Ehrenfest-like approach is employed, which allows the system to be in a coherent superposition. Tully's fewest switches surface hopping (FSSH) is used for the weak- and no-coupling regimes to improve the asymptotic behavior of the method. The decision of which approach to employ at a given time is made based on a simple analysis of Rabi oscillations in a two-state model. The method is tested for two exactly solvable model systems, i.e., a stimulated emission scenario in a pulsed laser field and a photoexcitation scenario in a cw laser field. Position and momentum densities of the nuclei compare well with exact quantum dynamics simulations and improve on both a pure Ehrenfest and a pure FSSH approach. The method is efficient and easily implemented.

We consider quasi-one-dimensional dipolar spinor Bose-Einstein condensates in the homogeneous-local-spin-orientation approximation, that is, with unidirectional local magnetization. By analytically calculating the exact effective dipole-dipole interaction, we derive a Landau-Lifshitz-Gilbert equation for the dissipative condensate magnetization dynamics, and show how it leads to the Stoner-Wohlfarth model of a uniaxial ferromagnetic particle, where the latter model determines the stable magnetization patterns and hysteresis curves for switching between them. For an external magnetic field pointing along the axial, long direction, we analytically solve the Landau-Lifshitz-Gilbert equation. The solution explicitly demonstrates that the magnetic dipole-dipole interaction accelerates the dissipative dynamics of the magnetic moment distribution and the associated dephasing of the magnetic moment direction. Under suitable conditions, dephasing of the magnetization direction due to dipole-dipole interactions occurs within time scales up to two orders of magnitude smaller than the lifetime of currently experimentally realized dipolar spinor condensates, e.g., those produced with the large magnetic-dipole-moment atoms ${}^{166}\mathrm{Er}$. This enables experimental access to the dissipation parameter $\mathrm{\Gamma }$ in the Gross-Pitaevskii mean-field equation, for a system currently lacking a complete quantum kinetic treatment of dissipative processes and, in particular, an experimental check of the commonly used assumption that $\mathrm{\Gamma }$ is a single scalar independent of spin indices.

We investigate the ground-state phase diagram and excitation spectrum of an interacting spinor Bose-Einstein condensate with spin-orbital-angular-momentum (SOAM) coupling realized in recent experiments by introducing atomic Raman transition with a pair of copropagating Laguerre-Gaussian laser beams that carry different orbital angular momenta (OAM) [Chen et al., Phys. Rev. Lett. 121, 113204 (2018) and Zhang et al., Phys. Rev. Lett. 122, 110402 (2019)]. Because of the ground-state degeneracy of the single-particle Hamiltonian at vanishing detuning, several angular-stripe phases, which are the superposition of states with different angular quantum numbers, appear in the phase diagram. However, these phases normally exist at small detuning, which makes them hard to be probed in experiments. We show that for a large OAM difference of the laser beams, an asymmetric kind of angular-stripe phase can exist even at large detuning. The excitation spectra in different phases exhibit distinct features: In the angular-stripe phase there exist two gapless bands corresponding to the broken $\mathrm{U}\left(1\right)$ and rotational symmetries, while in the half-skyrmion phase the gapless band exhibits a rotonlike structure. Our predictions of the angular-stripe phases and the low-energy excitations can be examined in recently realized Bose-Einstein condensates with SOAM coupling.

The spontaneous emission of an excited two-level emitter driven by a strong classical coherent low-frequency electromagnetic field is investigated. We find that for relatively strong laser driving, multiphoton processes are induced, thereby opening additional decay channels for the atom. We analyze the interplay between the strong low-frequency driving and the interfering multiphoton decay channels, and discuss its implications for the spontaneous emission dynamics.

We discuss bounds for nonadiabatic transitions from the viewpoints of the adiabatic perturbation theory and the quantum speed limit. We show that the amount of nonadiabatic transitions from the $n\mathrm{th}$ level to the $m\mathrm{th}$ level is bounded by a function of the quantum geometric tensor for the $m\mathrm{th}$ level. We analyze this bound from the viewpoint of the adiabatic perturbation theory. In addition, this bound and the viewpoint of the quantum speed limit suggest a nontrivial relationship between the dynamical transformation and the adiabatic transformation. We also derive a universal bound for any nonadiabatic transition. This bound is written in terms of the counterdiabatic Hamiltonian.

Machine learning has emerged as a promising approach to unveil properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods—such as Monte Carlo—which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data-reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented quantum algorithm recovers. Finally, we propose a majority vote quantum classifier built from a nearest-neighbor (checkerboard) quantum neural network. This classifier is successfully trained to recognize phases of matter with 99% accuracy for the transverse field Ising model and 94% accuracy for the $XXZ$ model. These findings suggest that a merger between quantum simulation and quantum enhanced machine learning offers a fertile ground to develop computational insights into quantum systems.

Transmission efficiency (TE) of remote state preparation (RSP) with a shared quantum state and one bit of classical communication is considered. Following Dakić et al. [Nat. Phys. 8, 666 (2012)], the encoding and decoding operators of the protocol are restricted to the physically relevant classes of projective measurements and unitary operators, respectively. It is shown that contrary to the previous arguments, the quadratic fidelity as well as the linear fidelity could be a valid figure of merit to quantify the TE of RSP. Then, the TE of the protocol in terms of both linear and quadratic fidelities is evaluated in a fully optimized scenario which includes the maximization over the encoding parameters as well as a meaningful maximization over the decoding parameters. The results show that, in this scenario, the TE scales with the sum of the two largest eigenvalues of the squared correlation matrix of the resource state that is zero only for product states. This approach successfully quantifies the performance of the protocol in terms of the resource state parameters and provides a means to compare the usefulness of any two resource states for RSP.

Gaussian boson sampling (GBS) is a near-term platform for photonic quantum computing. Applications have been developed that rely on directly programming GBS devices, but the ability to train and optimize circuits has been a key missing ingredient for developing new algorithms. In this work, we derive analytical gradient formulas for the GBS distribution, which can be used for training devices using standard methods based on gradient descent. We introduce a parametrization of the distribution that allows the gradient to be estimated by sampling from the same device that is being optimized. In the case of training using a Kullback-Leibler divergence or log-likelihood cost function, we show that gradients can be computed classically, leading to fast training. We illustrate these results with numerical experiments in stochastic optimization and unsupervised learning. As a particular example, we introduce the variational Ising solver, a hybrid algorithm for training GBS devices to sample ground states of a classical Ising model with high probability.

The time evolution of spin chains has been extensively studied for transferring quantum states between different registers of a quantum computer. Nonetheless, in most of these protocols only one sender-receiver pair can share the channel at each time. This significantly limits the rate of communication in a network of many users because they can only communicate through their common data-bus sequentially and not all at the same time. Here, we propose a protocol in which multiple users can share a spin chain channel simultaneously without having crosstalk between different parties. This is achieved by properly tuning the local parameters of the Hamiltonian to mediate an effective interaction between each pair of users via a distinct set of energy eigenstates of the system. We introduce three strategies with different levels of Hamiltonian tuning; each might be suitable for a different physical platform. All the three strategies provide very high transmission fidelities with vanishingly small crosstalk. The protocol is robust against various imperfections and we specifically show that our protocol can be experimentally realized on currently available superconducting quantum simulators.

A recently proposed classical-trajectory dynamical screening model for the description of multiple ionization and capture during ion–water-molecule collisions is extended to incorporate dynamical screening on both the multicenter target potential and the projectile ion. Comparison with available experimental data for $\mathrm{He}{}^{2+}$ $+$ $\mathrm{H}{}_2\mathrm{O}$ collisions at intermediate energies (10–150 keV/u) and $\mathrm{Li}{}^{3+}$ $+$ $\mathrm{H}{}_2\mathrm{O}$ at higher energies (100–850 keV/u) demonstrates the importance of both screening mechanisms. The question of how to deal with the repartitioning of the capture flux into allowed capture channels is addressed. The model also provides insights for data on highly charged projectile ions $(\mathrm{C}{}^{6+},$ $\mathrm{O}{}^{8+},$ $\mathrm{Si}{}^{13+})$ in the MeV/u range where the question of saturation effects in net ionization was raised in the literature.

We investigate theoretically the many-body pairing of a strongly correlated two-dimensional Fermi gas with and without negative confinement-induced effective range. Using a strong-coupling effective field theory in the normal state, we show that the specific heat at constant volume can be used as a characteristic indicator of the crossover from the normal Fermi liquid to the pseudogap state in two dimensions. We calculate the pseudogap formation temperature through the specific heat at constant volume, examining the role of a negative confinement-induced effective range on many-body pairing above the superfluid transition. We compare our results with and without effective range to the recent experimental measurement performed with radio-frequency spectroscopy in Murthy et al. [P. A. Murthy, M. Neidig, R. Klemt, L. Bayha, I. Boettcher, T. Enss, M. Holten, G. Zürn, P. M. Preiss, and S. Jochim, Science 359, 452 (2018)]. Although a good qualitative agreement is found, we are not able to discriminate the effect of the confinement-induced effect range in the experimental data.

We unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the dependence of the energy gaps on the anisotropy parameter. The relation between the two- and one-dimensional scattering lengths as well as the Tan contacts is established. The contact, capturing the two-body short-range correlations, shows an increasing tendency for a larger anisotropy. Subsequently, the interaction quench dynamics from attractive to repulsive values and vice versa is investigated for various anisotropies. A closed analytical form of the expansion coefficients of the two-body wave function, during the time evolution is constructed. The response of the system is studied by means of the time-averaged fidelity, the spectra of the spatial extent of the cloud in each direction, and the one-body density. It is found that as the anisotropy increases, the system becomes less perturbed independently of the interactions, while for fixed anisotropy quenches toward the noninteracting regime perturb the system in the most efficient manner. Furthermore, we identify that in the tightly confined direction more frequencies are involved in the dynamics stemming from higher lying excited states.

We obtain a master equation for a parametrically driven optomechanical cavity. We use a more correct dissipation model that accounts for the modification of the quasienergy spectrum caused by the driving. When the natural frequency of the mechanical object oscillates periodically around its mean value, the master equation with the improved dissipation model is expressed using Floquet operators. We apply the corresponding master equation to model the laser cooling of the mechanical object. Using an adiabatic approximation, an analytical expression for the number of excitations of the mechanical oscillator can be obtained. We find that the number of excitations can be lower than in the non-time-dependent case. Our results raise the possibility of achieving lower temperatures for the mechanical object if its natural frequency can be controlled as a function of time.

In this paper we use time-dependent Josephson coupling to enhance unconventional photon blockade in a system of two coupled nonlinear bosonic modes which are initially loaded with weakly populated coherent states, so the evolution is restricted to the manifold of up to two field quanta. Using numerical optimal control, we find the optimal coupling which minimizes the two-photon occupation of one mode, which is actually transferred to the other, while maintaining a nonzero one-photon occupation in the same mode. Moreover, we choose for the continuous coupling to vanish after the transfer between the modes such that they are decoupled and one of them is left only with some one-photon population which can be observed upon its decay. We numerically find lower values of the second-order correlation function obtained at earlier times than with constant coupling, with larger one-photon populations and for longer time windows, corresponding thus to higher emission efficiency and easier detection. The presented methodology is not restricted to the system under study, but it can also be transferred to other related frameworks, to find the optimal driving fields which can improve the single-photon emission statistics from these systems.