The design and optimization of realistic architectures for fault-tolerant quantum computation requires error models that are both reliable and amenable to large-scale classical simulation. Perhaps the simplest and most practical general-purpose method for constructing such an error model is to twirl a given completely positive channel over the Pauli basis, a procedure we refer to as the Pauli twirling approximation (PTA). In this work we test the accuracy of the PTA for a small stabilizer measurement circuit relevant to fault-tolerant quantum computation, in the presence of both intrinsic gate errors and decoherence, and find excellent agreement over a wide range of physical error rates. The combined simplicity and accuracy of the PTA, along with its direct connection to the $\chi$ matrix of process tomography, suggests that it can be used as a standard reference point for more refined error model constructions.

Antiproton ($\overline{p}$) collisions with hydrogen atoms, resulting in the hadronic process of particle-antiparticle annihilation and the atomic process of protonium ($\overline{p}p$) formation (or $\overline{p}$ capture), are investigated theoretically. As the collision energy decreases, the collision time required for the $\overline{p}$ capture becomes necessarily longer. Then, there is the possibility that the $\overline{p}$-$p$ annihilation occurs significantly before the $\overline{p}$ capture process completes. In such a case, one can no longer consider the annihilation decay separately from the $\overline{p}$ capture process. The present study develops a rigorous unified quantum-mechanical treatment of the annihilation and $\overline{p}$ capture processes. For this purpose, an $R$-matrix approach for atomic collisions is extended to have complex-valued $R$-matrix elements allowing for the hadronic annihilation. Detailed calculations are carried out at low collision energies ranging from ${10}^{-8}$ to ${10}^{-1}$ eV, and the annihilation and the $\overline{p}$ capture (total and product-state selected) cross sections are reported. Consideration is given to the difference between the direct annihilation occurring during the collision and the annihilation of $\overline{p}p$ occurring after the $\overline{p}$ capture. The present annihilation process is also compared with the annihilation in two-body $\overline{p}+p$ collisions.

In recent years diode laser sources have become widespread and reliable tools in magneto-optical spectroscopy. In particular, laser-driven atomic magnetometers have found a wide range of practical applications. More recently, so-called magnetically silent variants of atomic magnetometers have been developed. While in conventional magnetometers the magnetic resonance transitions between atomic sublevels are phase-coherently driven by a weak oscillating magnetic field, silent magnetometers use schemes in which either the frequency or the amplitude of the light beam is modulated. Here we present a theoretical model that yields algebraic expressions for the parameters of the multiple resonances that occur when either amplitude-, frequency-, or polarization-modulated light of circular polarization is used to drive the magnetic resonance transition in a transverse magnetic field. The relative magnitudes of the resonances that are observed in the transmitted light intensity at harmonic $m$ of the Larmor frequency ${\omega }_L$ (either by DC or phase sensitive detection at harmonics $q$ of the modulation frequency ${\omega }_{\mathrm{mod}}$) of the transmitted light are expressed in terms of the Fourier coefficients of the modulation function. Our approach is based on an atomic multipole moment representation that is valid for spin-oriented atomic states with arbitrary angular momentum $F$ in the low light power limit. We find excellent quantitative agreement with an experimental case study using (square-wave) amplitude-modulated light.

Using a combination of a fast two-dimensional-Hartree-Fock-Roothaan method and highly accurate fixed-phase diffusion quantum Monte Carlo simulations, we analyze the electronic structure and calculate the energy of the ground states of atoms with nuclear charges $Z=2–26$ in very strong magnetic fields $B={10}^7–5\times {10}^8\mathrm{T}$, relevant for astrophysical problems, e.g., the thermal emission of strongly magnetized isolated neutron stars.

Low-energy differential and integral cross sections for the electron-impact vibrational excitation of tetrahydrofuran are presented. The data concern four features in the vibrational excitation electron energy-loss spectrum of tetrahydrofuran over the energy-loss range of 0–0.9 eV. The results show weak influence from long-range dipole interactions, being mainly isotropic. Comparison with earlier work is presented.

This is a theoretical study of transmission of positrons of kinetic energies of 1 and 10 MeV through very short $(11,9)$ single-wall carbon nanotubes of lengths of 200 and 560 nm, respectively. The needed continuum interaction potential of the positron and nanotube is obtained starting from the Molière's approximation of the Thomas-Fermi interaction potential of a positron and a nanotube atom. We calculate the classical and quantum angular distributions of transmitted positrons. In the classical calculations, the approach is via the equations of motion, and in the quantum calculations, the time-dependent Schrödinger equation is solved. The solutions of these equations are obtained numerically. In the quantum calculations, the initial beam is taken to be an ensemble of noninteracting Gaussian wave packets. The angular distributions are generated using the computer simulation method. Our analysis is concentrated on the rainbow effect, which is clearly seen in the angular distributions. The obtained classical and quantum rainbows are analyzed in detail and compared with each other.

We study the energy exchange via electron correlation upon photon absorption over large distances in double photoionization of the helium dimer. Results of numerical simulations of the interaction of a planar helium dimer model with a short light pulse are found to be in good agreement with recent experimental data for the angular distribution of the emitted electron. The double ionization probability is closely related to that of the photoemission of an electron from one of the helium atoms along the internuclear axis. Together with an analysis of the temporal evolution of the two-electron probability distribution this provides direct evidence for the knockoff mechanism by which the photon energy is shared between the electrons over distances of several Angstroms in the dimer.

Ultracold atoms are trapped circumferentially on a ring that is pierced at its center by a flux tube arising from a light-induced gauge potential due to applied Laguerre-Gaussian fields. We show that by using optical coherent state superpositions to produce light-induced gauge potentials, we can create a situation in which the trapped atoms are simultaneously exposed to two distinct flux tubes, thereby creating superpositions in atomic quantum rings. We consider the examples of both a ring geometry and harmonic trapping, and in both cases the ground state of the quantum system is shown to be a superposition of counter-rotating states of the atom trapped on the two distinct flux tubes.

Roton excitations constitute a key feature of dipolar gases, connecting these gases with superfluid helium. We show that the density dependence of the roton minimum results in a spatial roton confinement, particularly relevant in pancake dipolar condensates with large aspect ratios. We show that roton confinement plays a crucial role in the dynamics after roton instability, and that arresting the instability may create a trapped roton gas revealed by confined density modulations. We discuss the local susceptibility against density perturbations, which we illustrate for the case of vortices. Roton confinement is expected to play a key role in experiments.

We suggest and demonstrate a technique to obtain relevant information about a composite system by performing measurements on only a small and easily accessible part of it, which we call a quantum probe. We show in particular how quantitative information about the angular correlations of pairs of entangled photons generated by spontaneous parametric down-conversion may be accessed through the study of the trace distance between two polarization states evolved from different initial conditions. After estimating the optimal polarization states to be used as the quantum probe, we provide a detailed analysis of the connections between the increase of the trace distance above its initial value and the amount of angular correlation.

We discuss the uniqueness of quantum states compatible with given measurement results for a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it was known that for a $d$-dimensional Hilbert space, there exists a set of $4d-5$ observables that uniquely determines any pure state. We show that for case (2), $5d-7$ observables suffice to uniquely determine any pure state. Thus, there is a gap between the results for (1) and (2), and we give some examples to illustrate this. Unique determination of a pure state by its reduced density matrices (RDMs), a special case of determination by observables, is also discussed. We improve the best-known bound on local dimensions in which almost all pure states are uniquely determined by their RDMs for case (2). We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low-rank quantum states.

The stationary multipartite entanglement between three interacting harmonic oscillators subjected to decoherence is analyzed in the largely unexplored nonequilibrium strong dissipation regime. We compute the exact asymptotic Gaussian state of the system and elucidate its separability properties, qualitatively assessing the regions of the space of parameters in which fully inseparable states are generated. Interestingly, the sharing structure of bipartite entanglement is seen to degrade as dissipation increases even for very low temperatures, at which the system approaches its ground state. We also find that establishing stationary energy currents across the harmonic chain does not correspond with the buildup of biseparable steady states, which relates instead just to the relative intensity of thermal fluctuations.

Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the $XY$ spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are respectively the real and imaginary parts of a complex-valued geometric entanglement, which can be investigated in typical quantum interferometry experiments. We argue that the singular behavior of the complex-value geometric entanglement at a quantum critical point is a characteristic of any quantum phase transition, by showing that the underlying mechanism is the occurrence of level crossings associated with the underlying Hamiltonian.

We introduce an ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Zémor and generalized bicycle codes by MacKay et al. as limiting cases. The construction allows for both the lower and the upper bounds on the minimum distance; they scale as a square root of the block length. Many thus defined codes have a finite rate and limited-weight stabilizer generators, an analog of classical low-density parity-check (LDPC) codes. Compared to the hypergraph-product codes, hyperbicycle codes generally have a wider range of parameters; in particular, they can have a higher rate while preserving the estimated error threshold.

The turbulence-induced decay of orbital-angular-momentum (OAM) entanglement between two photons is investigated numerically and experimentally. To compare our results with previous work, we simulate the turbulent atmosphere with a single phase screen based on the Kolmogorov theory of turbulence. We consider two different scenarios: in the first only one of the two photons propagates through turbulence, and in the second both photons propagate through uncorrelated turbulence. Comparing the entanglement evolution for different OAM values, we found the entanglement to be more robust in turbulence for higher OAM values. We derive an empirical formula for the distance scale at which entanglement decays in terms of the scale parameters and the OAM value.

The total energies of 28 bound $S$, $P$, $D$, $F$, $G$, $H$, and $I$ states in the three-electron Li atom and Be${}^{+}$ ion, respectively, are determined with the use of the configuration interaction (CI) with Slater orbitals and $LS$ eigenfunctions and the Hylleraas-configuration-interaction (Hy-CI) methods. We discuss the construction and selection of the configurations in the wave functions, optimization of the orbital exponents, and advanced computational techniques. Finally, we have developed an effective procedure which allows one to determine the energies of the excited states in three-electron atoms and ions to high accuracy by using compact wave functions. For the ground and low-lying excited states our best accuracy was $\approx$$1\times {10}^{-6}$ a.u. with the Hy-CI method and $1\times {10}^{-4}$ a.u. for other excited states. Analogous accuracy of the CI method is substantially lower, $\approx$$1\times {10}^{-3}$ a.u. Rotationally excited (bound) states in the three-electron Li atom and Be${}^{+}$ ion are evaluated here to high accuracy.

Signatures of multi-keV $LMN$ dielectronic resonances in highly charged $3d^n$ ions of tungsten were detected in the intensity ratios of extreme-ultraviolet magnetic-dipole lines within ground configurations. The measurements were performed with an electron beam ion trap at beam energies of about 6 keV. Large-scale collisional-radiative modeling incorporating magnetic sublevels of autoionizing levels showed the significance of anisotropy effects due to the monodirectional propagation of the electron beam. The observation method allows simultaneous resolved registration of dielectronic resonances from several ions.

We investigate the factors that influence the usefulness of supersonic collisions of Bose-Einstein condensates as a potential source of entangled atomic pairs by analyzing the reduction of the number difference fluctuations between regions of opposite momenta. We show that nonmonochromaticity of the mother clouds is typically the leading limitation on number squeezing, and that the squeezing becomes less robust to this effect as the density of pairs grows. We develop a simple model that explains the relationship between density correlations and the number squeezing, allows one to estimate the squeezing from properties of the correlation peaks, and shows how the multimode nature of the scattering must be taken into account to understand the behavior of the pairing. We analyze the impact of the Bose enhancement on the number squeezing, by introducing a simplified low-gain model. We conclude that as far as squeezing is concerned the preferable configuration occurs when atoms are scattered not uniformly but rather into two well-separated regions.

Intensity correlation measurements form the basis of many experiments based on spontaneous parametric down-conversion. In the most common situation, two single-photon avalanche diodes and coincidence electronics are used in the detection of the photon pairs, and the coincidence count distributions are measured by making use of some scanning procedure. Here we analyze the measurement of intensity correlations using multielement detector arrays. By considering the detector parameters such as the detection and noise probabilities, we found that the mean number of detected photons that maximizes the visibility of the two-photon correlations is approximately equal to the mean number of noise events in the detector array. We provide expressions predicting the strength of the measured intensity correlations as a function of the detector parameters and on the mean number of detected photons. We experimentally test our predictions by measuring far-field intensity correlations of spontaneous parametric down-conversion with an electron multiplying charge-coupled device camera, finding excellent agreement with the theoretical analysis.

We present an improved phase estimation scheme employing entangled SU(1,1) coherent states in comparison to NOON and entangled coherent states under perfect and lossy conditions for a fixed mean photon number. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized nonlinearity of the phase shifts, both without and with losses. Furthermore, we show that these states give the smallest variance in the phase parameter for a large number of photons in a different order of nonlinearity. Finally, the phase sensitivity of this interferometric setting with parity detection is discussed.