  We have developed a framework for using quantum annealing computation to
evaluate a key quantity in ionic diffusion in solids, the correlation factor.
Existing methods can only calculate the correlation factor analytically in the
case of physically unrealistic models, making it difficult to relate
microstructural information about diffusion path networks obtainable by current
${ab\ initio}$ techniques to macroscopic quantities such as diffusion
coefficients. We have mapped the problem into a quantum spin system described
by the Ising Hamiltonian. By applying our framework in combination with ab
initio technique, it is possible to understand how diffusion coefficients are
controlled by temperatures, pressures, atomic substitutions, and other
factors.We have calculated the correlation factor in a simple case with a known
exact result by a variety of computational methods, including simulated quantum
annealing on the spin models, the classical random walk, the matrix
description, and quantum annealing on D-Wave with hybrid solver. This
comparison shows that all the evaluations give consistent results with each
other, but that many of the conventional approaches require infeasible
computational costs. Quantum annealing is also currently infeasible because of
the cost and scarcity of Q-bits, but we argue that when technological advances
alter this situation, quantum annealing will easily outperform all existing
methods.
