Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability

TL;DR

This paper investigates how open-system quantum annealing can succeed in solving problems with exponentially small gaps, showing success is linked to thermal excitations at the critical point rather than gap size.

Contribution

It reveals that open-system quantum annealing can overcome small gap challenges due to thermal effects, contrasting with closed-system expectations.

Findings

Success probability increases with sector size despite small gaps.

Thermal excitations at the critical point dominate the success behavior.

Open-system dynamics differ from thermal relaxation predictions.

Abstract

Closed-system quantum annealing is expected to sometimes fail spectacularly in solving simple problems for which the gap becomes exponentially small in the problem size. Much less is known about whether this gap scaling also impedes open-system quantum annealing. Here we study the performance of a quantum annealing processor in solving such a problem: a ferromagnetic chain with sectors of alternating coupling strength that is classically trivial but exhibits an exponentially decreasing gap in the sector size. The gap is several orders of magnitude smaller than the device temperature. Contrary to the closed-system expectation, the success probability rises for sufficiently large sector sizes. The success probability is strongly correlated with the number of thermally accessible excited states at the critical point. We demonstrate that this behavior is consistent with a quantum open-system description that is unrelated to thermal relaxation, and is instead dominated by the system's properties at the critical point.