Gate-error analysis in simulations of quantum computers with transmon qubits

In the model of gate-based quantum computation, the qubits are controlled by a sequence of quantum gates. In superconducting qubit systems, these gates can be implemented by voltage pulses. The success of implementing a particular gate can be expressed by various metrics such as the average gate fidelity, the diamond distance, and the unitarity. We analyze these metrics of gate pulses for a system of two superconducting transmon qubits coupled by a resonator, a system inspired by the architecture of the IBM Quantum Experience. The metrics are obtained by numerical solution of the time-dependent Schr\"odinger equation of the transmon system. We find that the metrics reflect systematic errors that are most pronounced for echoed cross-resonance gates, but that none of the studied metrics can reliably predict the performance of a gate when used repeatedly in a quantum algorithm

6^6Li in a Three-Body Model with Realistic Forces: Separable vs. Non-separable Approach

{\bf Background:} Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. {\bf Purpose:} Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that their solution based on separable interactions agrees exactly with solutions based on non-separable forces. {\bf Results:} The ground state of $^6$Li is calculated via momentum space Faddeev equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-$^4$He force. For the latter the Pauli-forbidden $S$-wave bound state is projected out. This result is compared to a calculation in which the interactions in the two-body subsystems are represented by separable interactions derived in the Ernst-Shakin-Thaler framework. {\bf Conclusions:} We find that calculations based on the separable representation of the interactions and the original interactions give results that agree to four significant figures for the binding energy, provided an off-shell extension of the EST representation is employed in both subsystems. The momentum distributions computed in both approaches also fully agree with each other

Eigenstate Thermalization Hypothesis and Quantum Jarzynski Relation for Pure Initial States

Since the first suggestion of the Jarzynski equality many derivations of this equality have been presented in both, the classical and the quantum context. While the approaches and settings greatly differ from one to another, they all appear to rely on the initial state being a thermal Gibbs state. Here, we present an investigation of work distributions in driven isolated quantum systems, starting off from pure states that are close to energy eigenstates of the initial Hamiltonian. We find that, for the nonintegrable system in quest, the Jarzynski equality is fulfilled to good accuracy.Comment: 9 pages, 7 figure

Quantum Decoherence at Finite Temperatures

We study measures of decoherence and thermalization of a quantum system $S$ in the presence of a quantum environment (bath) $E$. The whole system is prepared in a canonical thermal state at a finite temperature. Applying perturbation theory with respect to the system-environment coupling strength, we find that under common Hamiltonian symmetries, up to first order in the coupling strength it is sufficient to consider the uncoupled system to predict decoherence and thermalization measures of $S$. This decoupling allows closed form expressions for perturbative expansions for the measures of decoherence and thermalization in terms of the free energies of $S$ and of $E$. Numerical results for both coupled and decoupled systems with up to 40 quantum spins validate these findings.Comment: 5 pages, 3 figure

Relativistic Harmonic Oscillator

We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum, its eigenfunctions in compact form, i. e., as power series, with expansion coefficients determined by an explicitly given recurrence relation. The corresponding eigenvalues are fixed by the requirement of normalizability of the solutions.Comment: 14 pages, extended discussion of result

Dynamo quenching due to shear flow

We provide a theory of dynamo (α effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the α effect is reduced by the shear even in the absence of magnetic field. The α effect is further suppressed by magnetic fields well below equipartition (with the large-scale flow) with different scalings depending on the relative strength of shear and magnetic field. The turbulent viscosity is also found to be significantly reduced by shear and magnetic fields, with positive value. These results suggest a crucial effect of shear and magnetic field on dynamo quenching and momentum transport reduction, with important implications for laboratory and astrophysical plasmas, in particular, for the dynamics of the Sun

An Asymptotic Preserving Scheme for the Euler equations in a strong magnetic field

This paper is concerned with the numerical approximation of the isothermal Euler equations for charged particles subject to the Lorentz force. When the magnetic field is large, the so-called drift-fluid approximation is obtained. In this limit, the parallel motion relative to the magnetic field direction splits from perpendicular motion and is given implicitly by the constraint of zero total force along the magnetic field lines. In this paper, we provide a well-posed elliptic equation for the parallel velocity which in turn allows us to construct an Asymptotic-Preserving (AP) scheme for the Euler-Lorentz system. This scheme gives rise to both a consistent approximation of the Euler-Lorentz model when epsilon is finite and a consistent approximation of the drift limit when epsilon tends to 0. Above all, it does not require any constraint on the space and time steps related to the small value of epsilon. Numerical results are presented, which confirm the AP character of the scheme and its Asymptotic Stability

Coulomb Distortion Effects for (e,e'p) Reactions at High Electron Energy

We report a significant improvement of an approximate method of including electron Coulomb distortion in electron induced reactions at momentum transfers greater than the inverse of the size of the target nucleus. In particular, we have found a new parametrization for the elastic electron scattering phase shifts that works well at all electron energies greater than 300 $MeV$. As an illustration, we apply the improved approximation to the $(e,e'p)$ reaction from medium and heavy nuclei. We use a relativistic ``single particle'' model for $(e,e'p)$ as as applied to $^{208}Pb(e,e'p)$ and to recently measured data at CEBAF on $^{16}O(e,e'p)$ to investigate Coulomb distortion effects while examining the physics of the reaction.Comment: 14 pages, 3 figures, PRC submitte

Borel-Moore motivic homology and weight structure on mixed motives

By defining and studying functorial properties of the Borel-Moore motivic homology, we identify the heart of Bondarko-H\'ebert's weight structure on Beilinson motives with Corti-Hanamura's category of Chow motives over a base, therefore answering a question of Bondarko