Change-over switch for quantum states transfer with topological channels in a circuit-QED lattice

We propose schemes to realize robust quantum states transfer between distant resonators using the topological edge states of a one-dimensional circuit quantum electrodynamics(QED)lattice.Analyses show that the distribution of edge states can be regulated accordingly with the on-site defects added on the resonators.And we can achieve different types of quantum state transfer without adjusting the number of lattices.Numerical simulations demonstrate that the on-site defects can be used as a change-over switch for high-fidelity single-qubit and two-qubit quantum states transfer.This work provides a viable prospect for flexible quantum state transfer in solid-state topological quantum system.

Quantum droplets in two-dimensional optical lattices

We study the stability of zero-vorticity and vortex lattice quantum droplets(LQDs),which are de-scribed by a two-dimensional(2D)Gross-Pitaevskii(GP)equation with a periodic potential and Lee-Huang-Yang(LHY)term.The LQDs are divided in two types:onsite-centered and offsite-centered LQDs,the centers of which are located at the minimum and the maximum of the potential,respec-tively.The stability areas of these two types of LQDs with diferent number of sites for zero-vorticity and vorticity with S=1 are given.We found that the μ-N relationship of the stable LQDs with a fixed number of sites can violate the Vakhitov-Kolokolov(VK)criterion,which is a necessary stability condition for nonlinear modes with an attractive interaction.Moreover,the μ-N relationship shows that two types of vortex LQDs with the same number of sites are degenerated,while the zero-vorticity LQDs are not degenerated.It is worth mentioning that the offsite-centered LQDs with zero-vorticity and vortex LQDs with S=1 are heterogeneous.

The Hyperbolic Schrödinger Equation and the Quantum Lattice Boltzmann Approximation

The quantum lattice Boltzmann(qlB)algorithm solves the 1D Dirac equations and has been used to solve approximately the classical(i.e.,non-relativistic)Schrödinger equation.We point out that the qlB method actually approximates the hyperbolic version of the non-relativistic Schrödinger equation,whose solution is thus obtained at the price of an additional small error.Such an error is of order of(ωCτ)-1,where ω_(C):=mc^(2)/h is the Compton frequency,h being the reduced Planck constant,m the rest mass of the electrons,c the speed of light,andτa chosen reference time(i.e.,1 s),and hence it vanishes in the non-relativistic limit c→+∞.This asymptotic result comes from a singular perturbation process which does not require any boundary layer and,consequently,the approximation holds uniformly,which fact is relevant in view of numerical approximations.We also discuss this occurrence more generally,for some classes of linear singularly perturbed partial differential equations.

The Quantum Lattice Boltzmann Equation:Recent Developments

The derivation of the quantum lattice Boltzmann model is reviewed with special emphasis on recent developments of the model,namely,the extension to a multi-dimensional formulation and the application to the computation of the ground state of the Gross-Pitaevskii equation(GPE).Numerical results for the linear and nonlinear Schr odinger equation and for the ground state solution of the GPE are also presented and validated against analytical results or other classical schemes such as Crank-Nicholson.

LATTICE QUANTUM CHROMODYNAMICS

Updated September 2013 by S. Hashimoto （KEK）, J. Laiho （Syracuse University）, and S.R. Sharpe （University of Washington）. 18.1. Lattice regularization of QCD

An Effective Way for Determining the Transition Points in Lattice QCD at Finite Temperature

The transition points of lattice quantum chromodynamics（QCD） with two degenerate flavors of Wilson quarks at finite temperature T and small imaginary quark chemical potential μ are determined by using the reweighting technique.Under the positive fermion determinant,i.e.,the chemical potential is pure imaginary,the simulations are performed at hopping parameter κ = 0.165.The comparison between the reweighting technique and the conventional point-by-point scanning method is presented.The results prove that the reweighting technique is an effective and efficient method in investigating the critical phenomenon.