In order to exploit quantum advantages, quantum algorithms are indispensable for operating machine learning with quantum computers. We here propose an intriguing hybrid approach of quantum information processing for quantum linear regression, which utilizes both discrete and continuous quantum variables, in contrast to existing wisdoms based solely upon discrete qubits. In our framework, data information is encoded in a qubit system, while information processing is tackled using auxiliary continuous qumodes via qubit-qumode interactions. Moreover, it is also elaborated that finite squeezing is quite helpful for efficiently running the quantum algorithms in a realistic setup. Comparing with an all-qubit approach, the present hybrid approach is more efficient and feasible for implementing quantum algorithms, still retaining exponential quantum speed-up.

A bipartite state ${\rho }^{AB}$ has a $k$-symmetric extension if there exists a ($k+1$)-partite state ${\rho }^{A{B}_1{B}_2...B_k}$ with marginals ${\rho }^{A{B}_i}={\rho }^{AB},\forall i$. The $k$-symmetric extension is called bosonic if ${\rho }^{A{B}_1{B}_2...B_k}$ is supported on the symmetric subspace of $B_1{B}_2...B_k$. Understanding the structure of symmetric and bosonic extension has various applications in the theory of quantum entanglement, quantum key distribution, and the quantum marginal problem. In particular, bosonic extension gives a tighter bound for the quantum marginal problem based on separability. In general, it is known that a ${\rho }^{AB}$ admitting symmetric extension may not have bosonic extension. In this work, we show that, when the dimension of the subsystem $B$ is 2 (i.e., a qubit), ${\rho }^{AB}$ admits a $k$-symmetric extension if and only if it has a $k$-bosonic extension. Our result has an immediate application to the quantum marginal problem and indicates a special structure for qubit systems based on group representation theory.

We derive a theory for the generation of arbitrary spin-spin interactions in superconducting circuits via periodic time modulation of the individual qubits or the qubit-qubit interactions. The modulation frequencies in our approach are in the microwave or radio-frequency regime, so the required fields can be generated with standard generators. Among others, our approach is suitable for generating spin lattices that exhibit quantum spin liquid behavior such as Kitaev's honeycomb model.

Quantum computers can efficiently simulate many-body systems. As a widely used Hamiltonian simulation tool, the Trotter-Suzuki scheme splits the evolution into the number of Trotter steps $N$ and approximates the evolution of each step by a product of exponentials of each individual term of the total Hamiltonian. The algorithmic error due to the approximation can be reduced by increasing $N$, which however requires a longer circuit and hence inevitably introduces more physical errors. In this work, we first study such a trade-off and numerically find the optimal number of Trotter steps $N_{\mathrm{opt}}$ given a physical error model in a near-term quantum hardware. Practically, physical errors can be suppressed using recently proposed error mitigation methods. We then extend physical error mitigation methods to suppress the algorithmic error in Hamiltonian simulation. By exploiting the simulation results with different numbers of Trotter steps $N\le N_{\mathrm{opt}}$, we can infer the exact simulation result within a higher accuracy and hence mitigate algorithmic errors. We numerically test our scheme with a five-qubit system and show significant improvements in the simulation accuracy by applying both physical and algorithmic error mitigations.

The rest-frame transition frequencies of the $6s{}^2{S}_{1/2}\to 6p{}^2{P}_{1/2}$ ($D_1$) and $6s{}^2{S}_{1/2}\to 6p{}^2{P}_{3/2}$ ($D_2$) lines in the stable isotopes of ${\mathrm{Ba}}^{+}$ were measured with an accuracy better than $200\mathrm{kHz}$ through (quasi)simultaneous collinear and anticollinear laser spectroscopy, leading to an improvement in the accuracy of the isotope shifts by more than an order of magnitude compared to previous data. The ratio of the field-shift constants in the $D_1$, $D_2$ fine-structure doublet has been determined to $f=1.0186\left(9\right)$ through a King plot analysis. These collinear laser spectroscopy measurements have reached an accuracy comparable to ion-trap measurements on allowed dipole transitions. Our result provides an accurate benchmark for atomic many-body calculations and is compared to pure Dirac-Hartree-Fock calculations and to elaborate multiconfigurational Dirac-Fock calculations. The influence of correlation effects and the Breit interaction on the isotope shift in ${\mathrm{Ba}}^{+}$ are discussed.

A discussion of basis sets consisting of exponentially decaying Coulomb Sturmian functions for modeling electronic structures is presented. The proposed basis-set construction selects Coulomb Sturmian functions using separate upper limits to their principal, angular momentum, and magnetic quantum numbers. Their common Coulomb Sturmian exponent is taken as a fourth parameter. The convergence properties of such basis sets are investigated taking the second- and third-row atoms at the Hartree-Fock level as examples. Thereby, important relations between the values of the basis-set parameters and the physical properties of the electronic structure are recognized. Furthermore, a connection between the optimal, i.e., minimum-energy, Coulomb Sturmian exponent and the average Slater exponents values obtained by Clementi and Raimondi [J. Chem. Phys. 38, 2686 (1963)] is made. These features of Coulomb Sturmian basis sets emphasize their ability to correctly reproduce the physical features of the Hartree-Fock wave functions. As an outlook, the application of Coulomb Sturmian discretizations for molecular calculations and post-Hartree-Fock methods is briefly discussed.

We propose a method to separate enantiomers using parity violation in the Casimir-Polder potential between chiral mirrors and chiral molecules. The proposed setup involves a molecular beam composed of chiral molecules passing through a planar cavity consisting of two chiral mirrors. Enantiomers of opposite handedness are deflected differently due to a chiral dependence of the Casimir-Polder potential, resulting in the separation of the enantiomers. Our setup provides an alternative experimental tool for enantiomer separation, as well as shedding light on the fundamental properties of the Casimir-Polder potential.

$R$-matrixcalculations of the electron collisions with a lithium atom at energies below the $3s$ excitation threshold are presented. The ${}^{1}S^e$, ${}^{3}S^e$, and ${}^{1}P^o$ phase shifts calculated in the near-threshold energy range are in excellent agreement with previous theoretical studies. The threshold behavior of the ${}^{3}P^o$ phase shift is accurately analyzed along with the resonance located at the scattering energy $\sim 60$ meV. The phase shifts and cross sections calculated here show two resonances below the $3s$ threshold that have not been previously reported.

We present the results of simulations of optical sideband cooling of atomic ions in a trap with a shallow potential well. In such traps, an ion cannot be Doppler cooled near to the Lamb-Dicke regime $\mathrm{[}{\eta }^2(2\langle n\rangle +1)\ll 1]$. Outside the Lamb-Dicke regime, the sideband cooling dynamics are altered by the existence of various Fock states with weak coupling where the cooling becomes very slow. A ${}^{40}\mathrm{Ca}^{+}$ ion trapped in our Penning trap realizes such a situation; hence single stage cooling is inefficient to prepare the ion in the motional ground state. For these systems, it is necessary to study the cooling dynamics in detail and we show that it is possible to implement an optimized cooling sequence to achieve efficient ground-state cooling. We also present the simulated cooling dynamics of two ions trapped in a Penning trap, where the presence of an additional motional mode requires a complicated cooling sequence in order to cool both axial modes to the ground state simultaneously. Additionally, we demonstrate the dissipative preparation of Fock states outside the Lamb-Dicke regime by sideband heating a single ion in a Penning trap.

Coherent control of two-state systems is traditionally achieved by resonant pulses of specific Rabi frequency and duration, by adiabatic techniques using level crossings or delayed pulses, or by sequences of pulses with precise relative phases (composite pulses). Here we develop a method for high-fidelity coherent control which uses a sequence of detuning pulses. By using the detuning pulse areas as control parameters, and driving on an analogy with composite pulses, we report a great variety of detuning pulse sequences for broadband and narrow-band transition probability profiles.

We present an approach for initiating and tracing ultrafast electron dynamics in core-excited atoms, molecules, and solids. The approach is based on stimulated resonant inelastic x-ray scattering induced by a single, chirped, broadband XUV or x-ray pulse. A first interaction with this pulse prepares a core-excited state wave packet by resonant core-excitation. A second interaction with the pulse at a later time induces the transition to valence-excited states, which is associated with stimulated emission. The preparation of the core-excited wave packet and the transition from the core-excited states to the valence-excited states occur at distinct chirp-dependent times. As a consequence, the stimulated emission carries information about the time evolution of the core-excited state wave packet.

Aiming at elucidating similarities and differences between quantum-optics biphoton interference phenomena and the quantum physics of quasi-one-dimensional double-well optically trapped ultracold neutral bosonic or fermionic atoms, we show that the analog of the optical biphoton joint-coincidence spectral correlations, studied with massless noninteracting biphotons emanating from Einstein-Podolsky-Rosen Bell-Bohm single-occupancy sources, corresponds to a distinct contribution in the total second-order momentum correlations of the massive, interacting, and time-evolving ultracold atoms. This single-occupancy contribution can be extracted from the total second-order momentum correlation function measured in time-of-flight experiments, which for the trapped atomic system contains, in general, a double-occupancy, NOON component. The dynamics of the two-particle system are modeled by a Hubbard Hamiltonian. The general form of this partial coincidence spectrum is a cosine-square quantum beating dependent on the difference of the momenta of the two particles, while the corresponding coincidence probability proper, familiar from its role in describing the Hong-Ou-Mandel coincidence dip of overlapping photons, results from an integration over the particle momenta. Because the second-order momentum correlations are mirrored in the time-of-flight spectra in space, our theoretical findings provide impetus for time-of-flight experimental protocols for emulating with (massive) ultracold atoms venerable optical interferometries that use two space-time separated and entangled (massless) photons or double-slit optical sources. The implementation of such developments will facilitate testing of fundamental aspects and enable applications of quantum physics with trapped massive ultracold atoms, that is, investigations of nonlocality and violation of Bell inequalities, entanglement, and quantum information science.

We introduce measures of quantum coherence as the speed of evolution of a system under decoherence. That is, coherence is the ability to estimate a dephasing channel, quantified by the quantum Fisher information. We extend the analysis to interferometric noise estimation, proving that quantum discord is the minimum sensitivity to local dephasing. A physically motivated set of free operations for discord is proposed. The amount of discord created by strictly incoherent operations is upper bounded by the initial coherence.

We report on collisions of multiply charged ions with free Bi nanoparticles in the gas phase. The nanoparticles contain up to 650 Bi atoms corresponding to a diameter of 3.5 nm. The stability limit of multiply charged Bi clusters has been investigated yielding appearance sizes for Bi clusters in charge states up to $q=6$, which are in good agreement with predictions of the liquid drop model. This finding underlines the metallic character of the Bi particles. By coincidence measurements the correlation between the dominant fragments ${\mathrm{Bi}}^{+}$ and ${{\mathrm{Bi}}_3}^{+}$ and larger multiply charged residues has been determined. The comparison of the kinetic energies with $Q$-value calculations within the liquid drop model allowed identifying specific decay processes as two-body asymmetric fission or multifragmentation events. The higher kinetic energies of singly charged monomer ions compared to that of trimer ions are explained by a higher fissility of the decaying system. Correlation islands for small fragments indicate different decay mechanisms based on two-step processes where a third undetected fragment can be emitted in the first or the second step.

Tunnel ionization rates of triplet Rydberg states in helium with principal quantum numbers close to 37 have been measured in electric fields at the classical ionization threshold of $\sim 197$ V/cm. The measurements were performed in the time domain by combining high-resolution continuous-wave laser photoexcitation and pulsed electric field ionization. The observed tunnel ionization rates range from ${10}^5$ to ${10}^7{\mathrm{s}}^{-1}$ and have, together with the measured atomic energy-level structure in the corresponding electric fields, been compared to the results of calculations of the eigenvalues of the Hamiltonian matrix describing the atoms in the presence of the fields to which complex absorbing potentials have been introduced. The comparison of the measured tunnel ionization rates with the results of these, and additional calculations for hydrogenlike Rydberg states performed using semiempirical methods, have allowed the accuracy of these methods of calculation to be tested. For the particular eigenstates studied the measured ionization rates are $\sim 5$ times larger than those obtained from semiempirical expressions.

Excitation of the isomeric nuclear state ${}^{229\mathrm{m}}\mathrm{Th}$ in the process of thorium atom irradiation by a two-color femtosecond pulse of a Ti:Sa laser at the fundamental wavelength and second harmonic ($\omega +2\omega$) is analyzed. It is shown that the rate of isomeric state excitation can be enhanced significantly with respect to other nucleus excitation processes in laser plasma or by an external coherent source at the resonance wavelength. This enhancement is due to the process of “nonlinear laser nuclear excitation,” which consists in excitation of a nuclear transition by e.m. radiation, generated by an electronic shell of the atom interacting with an intense laser field, with the photon energy coinciding with the nuclear transition energy. The process is based on the following. First, the atomic current associated with the motion of valence electrons in a strong $\omega +2\omega$ field is a nonlinear function of the field amplitude. Second, the energy of photons at the frequency of the Ti:Sa laser fifth harmonic coincides with the energy of the ${}^{229\mathrm{m}}\mathrm{Th}$ state. The yield of this harmonic is much higher if the two-color pulse (first and second harmonics of the fundamental) is used. Third, the intensity of the field produced by valence electrons at the atomic nucleus reaches the near-atomic value, which exceeds significantly the field strength associated with any other mechanism of laser plasma emission.

In one spatial dimension, quantum systems with an attractive three-body contact interaction exhibit a scale anomaly. In this work, we examine the few-body sector for up to six particles. We study those systems with a self-consistent, nonperturbative, iterative method in the subspace of zero total momentum. Exploiting the structure of the contact interaction, the method reduces the complexity of obtaining the wave function by three powers of the dimension of the Hilbert space. We present results on the energy, momentum, and spatial structure, as well as Tan's contact. We find a Fermi-Fermi crossover interpolating between large, weakly bound trimers and compact, deeply bound trimers: at weak coupling, the behavior is captured by degenerate perturbation theory; at strong coupling, the system is governed by an effective theory of heavy trimers (plus free particles in the case of asymmetric systems). Additionally, we find that there is no trimer-trimer attraction and therefore no six-body bound state.

It is well known that the reduced state of a two-mode squeezed vacuum state is a thermal state, i.e., a state whose photon-number statistics obey a geometric distribution. More exotic broadband states can be realized as the reduced state of two spectrally entangled beams generated using nonlinear optics. We show that these broadband “pseudothermal” states are tensor products of states in spectral Schmidt modes, whose photon-number statistics obey a geometric distribution. We study the spectral and temporal coherence properties of these states and show that their spectral coherence can be tuned—from perfect coherence to complete incoherence—by adjusting the pump spectral width. In the limit of a cw pump, these states are tensor products of true thermal states but with different temperatures at each frequency. This could be an interesting state of light for investigating the interplay between spectral, temporal, and photon-number coherences.

Using a recently developed technique based on the Rayleigh-Ritz optimization principle, we generate solitons for media with an arbitrary degree of nonlocality. We demonstrate that it is possible to obtain a plethora of complex self-trapped beams using known solutions to the harmonic oscillator for one-dimensional (1D), 2D, and 3D systems, but working directly with a generalized nonlinear nonlocal Schrödinger equation. We compare the parameters obtained variationally between the phenomenological Gaussian response and other more realistic nonlocal responses. We report that, for both kinds of nonlocal models, our approach obtains variational solutions that can remain self-trapped for certain conditions. We corroborate that, in general, the soliton dynamics can be different between the Gaussian response and the more realistic media for an arbitrary degree of nonlocality.