Recent work on Ising-coupled double-quantum-dot spin qubits in GaAs with voltage-controlled exchange interaction has shown improved two-qubit gate fidelities from the application of oscillating exchange along with a strong magnetic field gradient between adjacent dots [npj Quantum Inf. 3, 3 (2017)]. By examining how noise propagates in the time-evolution operator of the system, we find an optimal set of parameters that provide passive stroboscopic circumvention of errors in two-qubit gates to first order. We predict over 99% two-qubit gate fidelities in the presence of quasistatic and $1/f$ noise, which is an order-of-magnitude improvement over the typical unoptimized implementation.

We compare a conventional Mach–Zehnder light-pulse atom interferometer based on diffractive mirrors with one that uses specular reflection. In contrast to diffractive mirrors that generate a symmetric configuration, specular mirrors realized, for example, by evanescent fields lead under the influence of gravity to an asymmetric geometry. In such an arrangement the interferometer phase contains nonrelativistic signatures of proper time.

We investigate the one-dimensional mixture of scalar bosons and spin-polarized fermions interacting through a $\delta$-function potential. Using a thermodynamic description derived by employing a lattice embedding of the continuum model and the quantum transfer-matrix method, we perform a detailed analysis of the contact and quantum critical behavior. We show that the compressibility Wilson ratio presents anomalous enhancement at the quantum critical points and that the boundaries of the quantum critical regions can be well mapped by the maxima of the specific heat. As a function of the coupling strength and temperature, the contact presents nonmonotonic behavior. In the strong-coupling regime the local minimum exhibited by the contact as a function of temperature is accompanied by a significant momentum reconstruction at both low and high momenta. This momentum reconstruction occurs as the system crosses the boundary between the Tomonaga-Luttinger liquid phase to the spin-incoherent regime and provides an experimental signature of the transition.

In electromagnetic scattering, the so-called $T$ matrix encompasses the optical response of a scatterer for any incident excitation and is most commonly defined using the basis of multipolar fields. It can therefore be viewed as a generalization of the concept of polarizability of the scatterer. We calculate here the series expansion of the $T$ matrix for a spheroidal particle in the small-size, long-wavelength limit, up to third lowest order with respect to the size parameter, $\tilde{X}$, which we will define rigorously for a nonspherical particle. $\mathbf{T}$ is calculated from the standard extended boundary condition method with a linear system involving two infinite matrices $\mathbf{P}$ and $\mathbf{Q}$, whose matrix elements are integrals on the particle surface. We show that the limiting form of the $P$ and $Q$ matrices, which is different in the special case of spheroid, ensures that this Taylor expansion can be obtained by considering only multipoles of order 3 or less (i.e., dipoles, quadrupoles, and octupoles). This allows us to obtain self-contained expressions for the Taylor expansion of $\mathbf{T}\left(\tilde{X}\right)$. The lowest order is $O\left({\tilde{X}}^3\right)$ and equivalent to the quasistatic limit or Rayleigh approximation. Expressions to order $O\left({\tilde{X}}^5\right)$ are obtained by Taylor expansion of the integrals in $\mathbf{P}$ and $\mathbf{Q}$ followed by matrix inversion. We then apply a radiative correction scheme, which makes the resulting expressions valid up to order $O\left({\tilde{X}}^6\right)$. Orientation-averaged extinction, scattering, and absorption cross sections are then derived. All results are compared to the exact $T$-matrix predictions to confirm the validity of our expressions and assess their range of applicability. For a wavelength of 400 nm, the new approximation remains valid (within 1% error) up to particle dimensions of the order of $100\text{–}200$ nm depending on the exact parameters (aspect ratio and material). These results provide a relatively simple and computationally friendly alternative to the standard $T$-matrix method for spheroidal particles smaller than the wavelength, in a size range much larger than for the commonly used Rayleigh approximation.

We consider an arbitrary qubit channel depending on a single parameter, which is to be estimated by a physical process. Using the quantum Fisher information per channel invocation to quantify the estimation accuracy, we consider various estimation protocols when the available initial states are mixed with very low purity $r$. We compare a protocol using a single channel invocation on one out of $n$ qubits prepared in a particular correlated input state to the optimal protocol using uncorrelated input states, with the same initial-state purity. We show that, to lowest order in initial-state purity, for a unital channel this correlated-state protocol enhances the estimation accuracy by a factor between $n-1$ and $n$, provided that $n{r}^2\ll 1$. We also show that to lowest order in initial-state purity, a broad class of nonunital channels yields no gain regardless of the input state.

Continuous-variable (CV) devices are a promising platform for demonstrating large-scale quantum information protocols. In this framework we define a general quantum computational model based on a CV hardware. It consists of vacuum input states, a finite set of gates—including non-Gaussian elements—and homodyne detection. We show that this model incorporates encodings sufficient for probabilistic fault-tolerant universal quantum computing. Furthermore, we show that this model can be adapted to yield sampling problems that cannot be simulated efficiently with a classical computer, unless the polynomial hierarchy collapses. This allows us to provide a simple paradigm for experiments to probe quantum advantage relying on Gaussian states, homodyne detection, and some form of non-Gaussian evolution. We finally address the recently introduced model of instantaneous quantum computing in CV, and prove that the hardness statement is robust with respect to some experimentally relevant simplifications in the definition of that model.

We investigate the feasibility of single-shot Toffoli- and Fredkin-gate realizations in qubit arrays with Heisenberg-type exchange interactions between adjacent qubits. As follows from the Lie-algebraic criteria of controllability, such an array is rendered completely controllable—equivalent to allowing universal quantum computation—by a Zeeman-like control field with two orthogonal components acting on a single “actuator” qubit. Adopting this local-control setting, we start our analysis with piecewise-constant control fields and determine the global maxima of the relevant figure of merit (target-gate fidelity) by combining the multistart-based clustering algorithm and quasi-Newton type local optimization. We subsequently introduce important practical considerations, such as finite frequency bandwidth of realistic fields and their leakage away from the actuator. We find the shortest times required for high-fidelity Toffoli- and Fredkin-gate realizations and provide comparisons to their respective two-qubit counterparts—controlled-not and exponential-swap. In particular, the Toffoli-gate time compares much more favorably to that of controlled-not than in the standard decomposition-based approach. This study indicates that the use of the single-shot approach can alleviate the burden on control-generating hardware in future experimental realizations of multiqubit gates.

A space-time crystal has recently been observed in a superfluid Bose gas. Here we construct a variational model that allows us to describe from first principles the coupling between the radial breathing mode and the higher-order axial modes that underlies the observation of the space-time crystal. By comparing with numerical simulations we verify the validity of our variational Ansatz. From the model we determine the requirements for the observation of the space-time crystal and the Ising-like nature of the symmetry breaking involved. Also, we find the onset and growth rate of the space-time crystal, which can be compared to experiments.

We developed a comprehensive semiclassical theory of solitons in one-dimensional systems at the BCS-BEC crossover to provide a semiclassical explanation of their excitation spectra. Our semiclassical results agree well with the exact solutions on both the deep BCS and the deep BEC side and explain qualitatively the smooth crossover between them. Especially, we showed that the minimum energy of the $S=1/2$ excitation is achieved exactly at the Fermi momentum $k_F=\pi n/2$, where $n{m}_F$ ($m_F$ is the mass of the fermionic atom) is the total mass density of the system. This momentum remains unchanged along the whole crossover whether the mass is contained in the bosonic molecules as on the deep BEC side or in the fermionic atoms as on the deep BCS side. This phenomenon comes about as a result of a special feature of one-dimensional systems that the conventional quasiparticle is not stable with respect to soliton formation. It is valid not only in exactly solvable models, but also on the level of semiclassical theory. Besides, we also resolved the inconsistency of existing semiclassical theory with the exact solution of solitonlike $S=0$ excitations on the deep BCS side by a different proposal of soliton configuration.

The impact of the carrier-envelope phase (CEP) of a long relativistic tightly focused laser pulse on the dynamics of a counterpropagating electron beam has been investigated theoretically in the, so-called, electron reflection regime. Our semiclassical Monte Carlo simulations show that the electrons are reflected at the rising edge of the laser pulse due to the ponderomotive force of the focused laser beam, and an asymmetric electron-momentum distribution emerges along the laser polarization direction, which sensitively depends on the CEP of the driving laser pulse for weak radiative stochasticity effects. The CEP signatures can be determined in the electron-momentum distribution at laser intensities of the order or larger than ${10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ and for the pulse lengths up to 10 cycles. The CEP detection resolution is proportional to the electron beam density and can achieve approximately $0.1^{\circ }$ at an electron density of about ${10}^{15}{\mathrm{cm}}^{-3}$. The method is applicable for currently available ultraintense laser facilities with the laser peak power ranging from tens of terawatt to multipetawatt.

We demonstrate how to tailor the losses of nonlinear cavities in order to suppress their reflection and enhance their nonreciprocal transmission. We derive analytical expressions predicting the existence of zero-reflection channels in single and coupled nonlinear cavities, depending on the driving frequency and loss rates. While suppressing the reflection from a single cavity imposes a stringent condition on the input-output leakage rates, we demonstrate that this condition can be significantly relaxed in systems of coupled cavities. In particular, zero-reflection and nonreciprocity can be achieved across a range of driving frequencies in coupled cavities by tuning the output leakage rate alone. Numerical calculations based on the driven-dissipative Gross-Pitaevskii equation, usually employed to describe microcavity polaritons, reveal the spatial phenomenology associated with zero-reflection states and provide design guidelines for the construction of nonlinear optical isolators.

Spin-orbit interaction of light can lead to the so-called optical mirages, i.e., a perceived displacement in the position of a particle due to the spiraling structure of the scattered light. In electric dipoles, the maximum displacement is subwavelength and does not depend on the optical properties of the scatterer. Here we will show that the optical mirage in high refractive index dielectric nanoparticles depends strongly on the ratio between electric and magnetic dipolar responses. When the dual symmetry is satisfied (at the first Kerker condition), there is a considerable enhancement (far above the wavelength) of the spin-orbit optical mirage which can be related to the emergence of an optical vortex in the backscattering direction.

We present an unbiased numerical density-matrix renormalization group study of the one-dimensional Bose-Hubbard model supplemented by nearest-neighbor Coulomb interaction and bond dimerization. It places the emphasis on the determination of the ground-state phase diagram and shows that, besides dimerized Mott and density-wave insulating phases, an intermediate symmetry-protected topological Haldane insulator emerges at weak Coulomb interactions for filling factor one, which disappears, however, when the dimerization becomes too large. Analyzing the critical behavior of the model, we prove that the phase boundaries of the Haldane phase to Mott insulator and density-wave states belong to the Gaussian and Ising universality classes with central charges $c=1$ and $c=1/2$, respectively, and merge in a tricritical point. Interestingly we can demonstrate a direct Ising quantum phase transition between the dimerized Mott and density-wave phases above the tricritical point. The corresponding transition line terminates at a critical end point that belongs to the universality class of the dilute Ising model with $c=7/10$. At even stronger Coulomb interactions the transition becomes first order.

Using a Bayesian methodology, we introduce the maximum a posteriori probability (MAP) estimator for quantum state and process tomography. We show that the maximum likelihood, the hedged maximum likelihood, and the maximum likelihood-maximum entropy estimator, and estimators of this general type, can be viewed as special cases of the MAP estimator. The MAP, like the Bayes mean estimator, includes prior knowledge. For cases of interest to tomography MAP can take advantage of convex optimization tools, making it numerically tractable. We show how the MAP and other Bayesian quantum state estimators can be corrected for noise produced if the quantum state passes through a noisy quantum channel prior to measurement. Numerical simulations on a single qubit indicate that, on average, including these corrections significantly improves the estimate even when the measurement data are modestly large.

In this paper, we study the local distinguishability of mutually orthogonal product quantum states with entanglement as a valuable resource. We present protocols in which entanglement is used more efficiently than in the previous protocols presented by Zhang et al. [Phys. Rev. A 97, 022334 (2018)]. Specifically, the main technical contributions are as follows: First, we present a method to locally distinguish a set of orthogonal product quantum states in $d\otimes d$ ($d$ is odd) by using only one ancillary two-qubit maximally entangled state. Then we present a similar method to locally distinguish multipartite orthogonal product states by using entanglement efficiently. Moreover, we propose a method to study the local distinguishability of this kind of orthogonal product state with less than one ebit of entanglement, and analyze the relationship between the probability of error and the quantity of entanglement, which reveals the phenomenon of less nonlocality with more entanglement.

Nuclei with a quadrupole deformation, such as ${}^{177}\mathrm{Hf}$ have enhanced weak quadrupole moment which induces the tensor weak electron-nucleus interaction in atoms and molecules. Corresponding parity-non-conserving (PNC) effect is strongly enhanced in the ${}^3{\mathrm{\Delta }}_1$ electronic state of the ${}^{177}\mathrm{HfF}^{+}$ cation which has very close opposite parity levels mixed by this tensor interaction. In the present paper we perform relativistic many-body calculations of this PNC effect. It is shown that the tensor weak interaction induced by the weak quadrupole moment gives the dominating contribution to the PNC effects in ${}^{177}\mathrm{HfF}^{+}$ which significantly exceeds contributions of the vector anapole moment and the scalar weak charge. The anapole and the weak charge can contribute due to the nonadiabatic mechanism proposed here. Therefore, corresponding experiment will allow one to separate the tensor weak PNC effect from the other PNC effects and to measure the quadrupole moment of the neutron distribution which gives the dominating contribution to the weak quadrupole moment.

A generalized Kohn-Sham (GKS) scheme which variationally minimizes the random phase approximation (RPA) ground-state energy with respect to the GKS one-particle density matrix is put forward. We introduce the notion of functional self-consistent schemes, which vary the one-particle Kohn-Sham (KS) potential entering an explicitly potential-dependent exchange-correlation (XC) energy functional for a given density, and distinguish them from orbital-self-consistent (OSC) schemes, which vary the density, or the orbitals, density matrix, or KS potential generating the density. It is shown that, for explicitly potential-dependent XC functionals, existing OSC schemes such as the optimized effective potential method violate the Hellmann-Feynman theorem for the density, producing a spurious discrepancy between the KS density and the correct Hellmann-Feynman density for approximate functionals. A functional self-consistency condition is derived which resolves this discrepancy by requiring the XC energy to be stationary with respect to the KS potential at fixed density. We approximately impose functional self-consistency by semicanonical projection (sp) of the Perdew, Burke, and Ernzerhof KS Hamiltonian. Variational OSC minimization of the resulting GKS-spRPA energy functional leads to a nonlocal correlation potential whose off-diagonal blocks correspond to orbital rotation gradients, while its diagonal blocks are related to the RPA self-energy at a real frequency. Quasiparticle $GW$ energies are a first-order perturbative limit of the GKS-spRPA orbital energies; the lowest-order change of the total energy captures the renormalized singles excitation correction to RPA. GKS-spRPA orbital energies are found to approximate ionization potentials and fundamental gaps of atoms and molecules more accurately than semilocal density functional approximations (SL DFAs) or $G_0{W}_0$ and correct the spurious behavior of SL DFAs for negative ions. GKS-spRPA energy differences are uniformly more accurate than the SL-RPA ones; improvements are modest for covalent bonds but substantial for weakly bound systems. GKS-spRPA energy minimization also removes the spurious maximum in the SL-RPA potential energy curve of ${\mathrm{Be}}_2$ and produces a single Coulson-Fischer point at $\sim 2.7$ times the equilibrium bond length in ${\mathrm{H}}_2$. GKS-spRPA thus corrects most density-driven errors of SL-RPA, enhances the accuracy of RPA energy differences for electron-pair-conserving processes, and provides an intuitive one-electron GKS picture yielding ionization potentials energies and gaps of $GW$ quality.

In previous research, we tested the wave-function format of a linear combination of several antisymmetrized geminal power states. A numerical problem in the geminal matrices was noted, which made the total energies of electronic systems with large numbers of electrons unstable. The underlying cause was found to be the large cancellation term in the geminal power series. We have obtained a format to resolve this problem for the case of total energies and partly for the first-order derivatives within the antisymmetrized geminal power states. By using this formalism, we have calculated the ground-state energies for several electronic systems, including the usage of a larger chemical basis set. The results are, in some cases, very close to the exact result, especially for one-dimensional Hubbard systems. Our result for a water molecule with the Dunning double zeta basis set is better than the configuration-interaction singles and doubles energy and approaches the coupled cluster singles and doubles energy.

We find that a donor-doped band-gap material can enhance the overall high-order harmonic generation (HHG) efficiency by several orders of magnitude, compared with undoped and acceptor-doped materials. This significant enhancement, predicted by time-dependent density functional theory simulations, originates from the highest occupied impurity state which has an isolated energy located within the band gap. The impurity-state HHG is rationalized by a three-step model, taking into account that the impurity-state electron tunnels into the conduction band and then moves according to its band structure until recombination. In addition to the improvement of the HHG efficiency, the donor-type doping results in a harmonic cutoff different from that in the undoped and acceptor-doped cases, explained by semiclassical analysis for the impurity-state HHG.