Rigorous convergence condition for quantum annealing

TL;DR

This paper establishes a rigorous mathematical bound on the rate at which the transverse field must decrease in quantum annealing to reliably find the ground state of a generic Ising model, ensuring convergence.

Contribution

It provides a rigorous, mathematically proven convergence condition for quantum annealing, improving upon previous asymptotic results and enabling better control for specific problems.

Findings

Derived a generic bound on the transverse field decrease rate for convergence.

Provided a rigorous upper bound on excitation probability in the infinite-time limit.

Established a sufficient condition for convergence applicable to any transverse-field Ising model.

Abstract

We derive a generic bound on the rate of decrease of transverse field for quantum annealing to converge to the ground state of a generic Ising model when quantum annealing is formulated as an infinite-time process. Our theorem is based on a rigorous upper bound on the excitation probability in the infinite-time limit and is a mathematically rigorous counterpart of a previously known result derived only from the leading-order term of the asymptotic expansion of adiabatic condition. Since our theorem gives a sufficient condition of convergence for a generic transverse-field Ising model, any specific problem may allow a better, faster, control of the coefficient.