Global warming: Temperature estimation in annealers

TL;DR

This paper evaluates methods to estimate the operational temperature range of quantum annealers, demonstrating their usefulness even when distributions deviate from ideal Boltzmann behavior due to ergodicity breaking.

Contribution

It introduces local and global temperature concepts and discusses analyzing annealers with post-processing to address practical distribution deviations.

Findings

Estimates of temperature ranges remain useful despite ergodicity breaking.

Different estimation methods capture local and global temperature variations.

Post-processing can help isolate practical distribution deviations.

Abstract

Sampling from a Boltzmann distribution is NP-hard and so requires heuristic approaches. Quantum annealing is one promising candidate. The failure of annealing dynamics to equilibrate on practical time scales is a well understood limitation, but does not always prevent a heuristically useful distribution from being generated. In this paper we evaluate several methods for determining a useful operational temperature range for annealers. We show that, even where distributions deviate from the Boltzmann distribution due to ergodicity breaking, these estimates can be useful. We introduce the concepts of local and global temperatures that are captured by different estimation methods. We argue that for practical application it often makes sense to analyze annealers that are subject to post-processing in order to isolate the macroscopic distribution deviations that are a practical barrier to their application.