Quantum annealing approach to Ionic Diffusion in Solid

Abstract

We developed a framework to evaluate a key quantity to describe the ionic diffusion in solids, the correlation factor, for which we can apply the quantum annealing computation to get rid of the current limitation for the evaluation being possible only for the simple models far from the practical diffusion paths. Though the current ab initio technique can provide the quantitative information about the diffusion paths network, the difficulty to evaluate the coefficient has hampered to connect such microscopic ab initio works with macroscopic quantities like diffusion coefficients. By applying the framework, we can evaluate how the diffusion coefficients are controlled by temperatures, pressures, atomic substitutions etc. when coupled with ab initio technique. We formulated the problem in terms of the mapping into a quantum spin systems described by the Ising Hamiltonian. Calibrating verifications to get a value of the coefficient already known for a simple model is performed on the comparisons amongst various possible methods including simulated quantum annealing on the spin models, the classical random walk, and the matrix description for the problem. We have confirmed that all the evaluations give consistent results with each other though some of the conventional approaches require infeasible computational costs supporting the advantage of the quantum annealing application.