Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core of which amounts to evaluating the logarithm of the marginal likelihood ($\mathrm{LML}$) of a given model. The $\mathrm{LML}$ gives a concrete measure of the quality of prediction that a GP model is expected to achieve. The classical computation of the $\mathrm{LML}$ typically carries a polynomial time overhead with respect to the input size. We propose a quantum algorithm that computes the logarithm of the determinant of a Hermitian matrix, which runs in logarithmic time for sparse matrices. This is applied in conjunction with a variant of the quantum linear system algorithm that allows for logarithmic-time computation of the form ${\mathbf{y}}^T{A}^{-1}\mathbf{y}$, where $\mathbf{y}$ is a dense vector and $A$ is the covariance matrix. We hence show that quantum computing can be used to estimate the $\mathrm{LML}$ of a GP with exponentially improved efficiency under certain conditions.

We study the results of a compiled version of Shor's factoring algorithm on the ibmqx5 superconducting chip, for the particular case of $N=15$, 21, and 35. The semiclassical quantum Fourier transform is used to implement the algorithm with only a small number of physical qubits, and the circuits are designed to reduce the number of gates to the minimum. We use the square of the statistical overlap to give a quantitative measure of the similarity between the experimentally obtained distribution of phases and the predicted theoretical distribution of phases for different values of the period. This allows us to assign a period to the experimental data without the use of the continued fraction algorithm. A quantitative estimate of the error in our assignment of the period is then given by the overlap coefficient.

Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an ordered sequence of graphs governs free evolution of the quantum walk. We then consider how perfect state transfer during the quantum walk can be used to design dynamic graphs that implement a universal set of quantum logic gates. We give explicit examples for a complete logical basis, and we validate implementations using numerical simulations for quantum teleportation and addition circuits. Finally, we discuss the potential for realizing CTQWs on dynamic graphs using actively controlled quantum optical waveguides.

Interfacing superconducting qubits with optical photons require noise-free microwave-to-optical transducers, a technology currently not realized at the single-photon level. We propose to use four-wave mixing in an ensemble of cold ytterbium (Yb) atoms prepared in the metastable “clock” state. The parametric process uses two high-lying Rydberg states for bidirectional conversion between a 10 GHz microwave photon and an optical photon in the telecommunication E-band. To avoid noise photons due to spontaneous emission, we consider continuous operation far detuned from the intermediate states. We use an input-output formalism to predict conversion efficiencies of $\approx 50\%$ with bandwidths of $\approx 100$ kHz.

Quantum coherence plays a fundamental and operational role in different areas of physics. A resource theory has been developed to characterize the coherence of distinguishable particles systems. Here we show that indistinguishability of identical particles is a source of coherence, even when they are independently prepared. In particular, under spatially local operations, states that are incoherent for distinguishable particles, can be coherent for indistinguishable particles under the same procedure. We present a phase discrimination protocol, in which we demonstrate the operational advantage of using two indistinguishable particles rather than distinguishable ones. The coherence due to the quantum indistinguishability significantly reduces the error probability of guessing the phase, using the most general measurements. The role played by particle statistics in the protocol is also investigated.

The understanding of the behavior of systems of identical composite bosons has progressed significantly in connection with the analysis of the entanglement between constituents and the development of coboson theory. The basis of these treatments is a coboson ansatz for the ground state of a system of $N$ pairs, stating that in appropriate limits this state is well approximated by the account of Pauli exclusion in what would otherwise be the product state of $N$ independent pairs, each described by the single-pair ground state. In this work we study the validity of this ansatz for particularly simple problems, and show that short-range attractive interactions in very dilute limits and a single-pair ground state with very large entanglement are not enough to render the ansatz valid. On the contrary, we find that the dimensionality of the problem plays a crucial role in the behavior of the many-body ground state.

Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On the one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled from them. On the other hand, it has been shown recently that some of these PPT states exhibit genuinely high-dimensional entanglement, i.e., they have a high Schmidt number. Here we investigate the ($d\times d$)-dimensional PPT states for $d\ge 4$ discussed recently by E. Sindici and M. Piani [Phys. Rev. A 97, 032319 (2018)]. By generalizing their methods to the calculation of Schmidt numbers, we show that a linear $d/2$ scaling of its Schmidt number in the local dimension $d$ can be attained.

Recent years have seen a growing interest in quantum codes in three dimensions (3D). One of the earliest proposed 3D quantum codes is the 3D toric code. It has been shown that 3D color codes can be mapped to 3D toric codes. The 3D toric code on a cubic lattice is also a building block for the welded code which has the highest energy barrier to date. Although well known, the performance of the 3D toric code has not been studied extensively. In this paper we propose efficient decoding algorithms for the 3D toric code on a cubic lattice with and without boundaries and report their performance for various quantum channels. We observe a threshold of $\gtrsim 12\%$ for the bit flip errors, $\approx 3\%$ for the phase flip errors, and 24.8% for the erasure channel. We also study the performance of the welded 3D toric code on the quantum erasure channel. We did not observe a threshold for the welded code over the erasure channel for the parameters we simulated.

The values of the nuclear electric quadrupole moment are different by about 7% for the ${}^{87}\mathrm{Sr}$ nucleus between the recommended value [Stone, At. Data Nucl. Data Tables 111-112, 1 (2016); Pyykkö, Mol. Phys. 116, 1328 (2018)] and earlier results [e.g., Mårtensson-Pendrill, J. Phys. B 35, 917 (2002); Yu, Wu, Gou, and Shi, Phys. Rev. A 70, 012506 (2004)]. In this paper, we report the value $Q\left({}^{87}\mathrm{Sr}\right)=328\left(4\right)$ mb, making use of our calculated electric-field gradients produced by electrons at the nucleus in combination with experimental values for hyperfine structures of the $5s5p{}^{3}P_{1,2}$ states of the neutral Sr atom. In the framework of the multiconfiguration Dirac-Hartree-Fock theory, the electron correlations were taken into account systematically so as to control the uncertainties of the electric-field gradient at about 1% level. The present result is different from the recommended value, but in excellent agreement with those by Måtensson-Pendrill and Yu et al.. We would recommend the present $Q$ value as a reference for ${}^{87}\mathrm{Sr}$.

The static electric dipole polarizability of a system is a measure of the binding of its electrons. In density functional theory calculations, this binding is weakened by the presence of unphysical self-interaction in the density functional approximation (DFA), leading to overestimates of polarizabilities. To investigate this systematically we compare polarizabilities for the atoms from H to Ar and their anions and cations calculated in several DFAs and the corresponding self-interaction-corrected (SIC) DFAs with experiment and with high-level quantum chemistry reference values. The SIC results are obtained using the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) method. Removing self-interaction generally leads to smaller polarizabilities that agree significantly better with reference values. We find that FLO-SIC improves the performance of the local spin density approximation and the generalized gradient approximation (GGA) for polarizabilities to a quality that is comparable to so-called rung 4 functionals, but slightly degrades the performance of the strongly constrained and appropriately normed meta-GGA functional.

The process of recombination for the hydrogen atom in the heat bath creating the blackbody radiation is described within the frameworks of quantum electrodynamics. For this purpose the self-energy for unbound electron in the field of the nucleus is considered. The imaginary part of this self-energy is directly connected with the recombination cross section. The same procedure is applied to the hydrogen atom in the field of blackbody radiation. This leads to a thermal correction to the process of recombination for the hydrogen atom in the heat bath.

Double-differential ionization cross sections (DDCS) for bare-carbon-ion-induced ionization of vapor-phase adenine molecules (${\text{C}}_5{\text{H}}_5{\text{N}}_5$) have been measured. The experiment has been performed using an electron spectroscopy technique. Electrons ejected from adenine were analyzed by a hemispherical electrostatic deflection analyzer over an energy range of $1\text{–}450\mathrm{eV}$ for emission angles from ${20}^{\circ }$ to ${160}^{\circ }$. The single-differential cross section (SDCS) and total ionization cross section were also deduced. The experimental results have been compared with the continuum distorted wave-eikonal initial-state model calculation. We have observed a very good agreement between the theory and experiment. The angular distribution of the DDCS, SDCS and the asymmetry parameter for low-energy ($E_e\le 0.5$ a.u.) electron display an oscillatory behavior which is in contrast to that observed in ion-atom collisions. A comparison is also made with available experimental cross-section results for uracil target colliding with the same velocity bare carbon ions and the scalability of ionization cross sections among these molecules is discussed.

We study polar alkali-metal dimer scattering in a quasi-one-dimensional geometry for both reactive and nonreactive species. Elastic and reactive rates are computed as a function of the amplitude of a static electric field within a purely long-range model with suitable boundary conditions at shorter range. We describe the diatomic molecules as rigid rotors and results are compared to the fixed-dipole approximation. We show in particular that for molecules with a sufficiently strong induced dipole moment oriented perpendicular to the trap axis, the long-range repulsive interaction leads to the suppression of short-range processes. Such shielding effect occurs for both reactive and nonreactive molecules, preventing two-body reactions as well as losses due to complex-mediated processes [M. Mayle et al., Phys. Rev. A 85, 062712 (2012)] from occurring. The present results demonstrate the possibility to suppress loss rates in current ultracold molecule experiments using one-dimensional confinement.

Charge dynamics in an ultracold setup involving a laser-dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange crucially depends on the coupling between the electronic dynamics and the motional dynamics of the atoms and ion. The molecular Rydberg states are characterized and a criterion for distinguishing coherent and incoherent regimes is formulated. Furthermore the concept is generalized to the many-body setup as the ion effectively propagates through a chain of atoms. Aspects of the transport, such as its direction, can be controlled by the excitation laser. This leads to new directions in the investigation of hybrid atom-ion systems that can be experimentally explored using optically trapped strontium atoms.

We investigate the nonequilibrium behavior of dilute, attractively interacting Fermi gases subjected to finite-duration ramps of their internal interaction strength. We identify three dynamical regimes as a function of ramp duration using a time-dependent version of the Bardeen-Cooper-Schrieffer theory of superconductivity to model these systems. For short ramp durations, these systems become nonsuperconducting; however, fermions with opposite momenta remain paired albeit with reduced amplitudes, and the associated pair amplitude distribution is nonthermal. In this first regime, the disappearance of superconductivity is due to the loss of phase coherence between pairs. By contrast, for intermediate ramp durations, superconductivity survives but the magnitude of the order parameter is reduced and presents long-lived oscillations. Finally, for long ramp durations, phase coherence is almost fully retained during the finite-duration interaction quench, and the steady state is characterized by a thermal-like pair amplitude distribution. Using this approach, one can therefore dynamically tune the coherence between pairs to control the magnitude of the superconducting order parameter and even engineer a nonequilibrium state made of preformed pairs.

The subject of bianyon interference with ultracold atoms is introduced through theoretical investigations pertaining to the second-order momentum correlation maps of two anyons (built upon spinless and spin-1/2 bosonic as well as spin-1/2 fermionic ultracold atoms) trapped in a double-well optical trap. The two-particle system is modeled according to the recently proposed protocols for emulating an anyonic Hubbard Hamiltonian in ultracold-atom one-dimensional lattices. Because the second-order momentum correlations are mirrored in the time-of-flight second-order interference patterns in space, our findings provide impetus for time-of-flight experimental protocols for detecting anyonic statistics via interferometry measurements of massive particles that broaden the scope of the biphoton interferometry of quantum optics.

We investigate the dynamical behavior of a self-pulsing laser under the influence of stimulated Brillouin scattering (SBS), a system which has previously been shown to favor extreme statistics. Using a laser model coupling a multi-Stokes Brillouin scattering process with the population inversion formalism for the gain and taking into account saturable absorption effects, we demonstrate that different statistical distribution types arise as the nonlinear interactions between the laser and higher-order SBS waves lead to the occurrence of high intensity short pulses. By taking into account up to five Stokes orders, we show that highly skewed statistics and pulses with extreme peak intensities can be obtained, allowing us to describe more accurately the experimental observations and to better apprehend the underlying physics. We also unexpectedly demonstrate that the acoustic noise does not affect the emergence of such extreme events.

In the emerging field of cavity optomagnonics, photons are coupled coherently to magnons in solid-state systems. These new systems are promising for implementing hybrid quantum technologies. Being able to prepare Fock states in such platforms is an essential step towards the implementation of quantum information schemes. We propose a magnon-heralding protocol to generate a magnon Fock state by detecting an optical cavity photon. Due to the peculiarities of the optomagnonic coupling, the protocol involves two distinct cavity photon modes. Solving the quantum Langevin equations of the coupled system, we show that the temporal scale of the heralding is governed by the magnon-photon cooperativity and derive the requirements for generating high fidelity magnon Fock states. We show that the nonclassical character of the heralded state, which is imprinted in the autocorrelation of an optical “read” mode, is only limited by the magnon lifetime for small enough temperatures. We address the detrimental effects of nonvacuum initial states, showing that high fidelity Fock states can be achieved by actively cooling the system prior to the protocol.

The quantum Rabi model accepts analytical solutions in the so-called degenerate qubit and relativistic regimes with discrete and continuous spectrum, in that order. We show that solutions are the superposition of even and odd displaced number states, in the former, and infinitely squeezed coherent states, in the latter, of the boson field correlated to the internal states of the qubit. We propose a single parameter model that interpolates between these discrete and continuous spectrum regimes to study the spectral statistics for first and second neighbor differences before the so-called spectral collapse. We find two central first neighbor differences that interweave and fluctuate keeping a constant second neighbor separation.

We examine quantum interference effects due to absorption and emission from multiple atoms coupled to a waveguide and highlight the modifications they entail with regard to single-photon transport properties. A prominent upshot of these interference phenomena is the resonant suppression of the reflection amplitude, which leads to the observation of multiple Fano minima in the reflection spectrum. Such minima determine the points at which transparency is induced in the system. By taking recourse to the real-space Hamiltonian framework, we calculate analytically the reflectivity and transmissivity for a one-dimensional waveguide that evanescently couples to a chain of equally spaced quantum emitters. The interemitter spacing relative to the wavelength of the propagating photon, leading to a waveguide-mediated “phase coupling” between the atoms, is found to fundamentally affect the existence of Fano minima. For a chain of $N$ atoms, the number of minima can be at most $N-1$. However, suitable choices of the phase can suppress the discernibility of the full range of roots in the reflection spectrum. A principal observation for the case of multiple emitters is the emergence of super-Gaussian characteristics close to zero detuning and, consequently, a plateau-shaped broadband spectrum in the region of high reflectivity. For a large chain size, the plateau gets transformed into a flat-topped quasirectangular profile in the frequency domain.