Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning

TL;DR

This paper introduces an effective-temperature estimation method for quantum annealers used in sampling tasks, demonstrating improved deep learning model training by accounting for instance-dependent temperatures, and compares it favorably to traditional contrastive divergence methods.

Contribution

The paper presents a novel simple algorithm to estimate the instance-dependent effective temperature of quantum annealers for sampling, improving their application in deep learning.

Findings

Effective-temperature estimation enhances quantum annealer sampling accuracy.

Instance-dependent temperatures lead to performance comparable to 100-step contrastive divergence.

The proposed method outperforms fixed-temperature assumptions in deep learning tasks.

Abstract

An increase in the efficiency of sampling from Boltzmann distributions would have a significant impact on deep learning and other machine-learning applications. Recently, quantum annealers have been proposed as a potential candidate to speed up this task, but several limitations still bar these state-of-the-art technologies from being used effectively. One of the main limitations is that, while the device may indeed sample from a Boltzmann-like distribution, quantum dynamical arguments suggest it will do so with an {\it instance-dependent} effective temperature, different from its physical temperature. Unless this unknown temperature can be unveiled, it might not be possible to effectively use a quantum annealer for Boltzmann sampling. In this work, we propose a strategy to overcome this challenge with a simple effective-temperature estimation algorithm. We provide a systematic study assessing the impact of the effective temperatures in the learning of a special class of a restricted Boltzmann machine embedded on quantum hardware, which can serve as a building block for deep-learning architectures. We also provide a comparison to $k$-step contrastive divergence (CD-$k$) with $k$ up to 100. Although assuming a suitable fixed effective temperature also allows us to outperform one step contrastive divergence (CD-1), only when using an instance-dependent effective temperature do we find a performance close to that of CD-100 for the case studied here.