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

Marcello Benedetti, John Realpe-Gómez, Rupak Biswas, and Alejandro Perdomo-Ortiz
Phys. Rev. A 94, 022308 – Published 9 August 2016

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 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.

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  • Received 27 March 2016
  • Revised 7 June 2016

DOI:https://doi.org/10.1103/PhysRevA.94.022308

©2016 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Marcello Benedetti

  • Quantum Artificial Intelligence Laboratory, NASA Ames Research Center, Moffett Field, California 94035, USA; SGT Inc., 7701 Greenbelt Road, Suite 400, Greenbelt, Maryland 20770, USA; and Department of Computer Science, University College London, WC1E 6BT London, United Kingdom

John Realpe-Gómez

  • Quantum Artificial Intelligence Laboratory, NASA Ames Research Center, Moffett Field, California 94035, USA; SGT Inc., 7701 Greenbelt Road, Suite 400, Greenbelt, Maryland 20770, USA; and Instituto de Matemáticas Aplicadas, Universidad de Cartagena, Bolívar 130001, Colombia

Rupak Biswas

  • Exploration Technology Directorate, NASA Ames Research Center, Moffett Field, California 94035, USA

Alejandro Perdomo-Ortiz*

  • Quantum Artificial Intelligence Laboratory, NASA Ames Research Center, Moffett Field, California 94035, USA and University of California, Santa Cruz, at NASA Ames Research Center, Moffett Field, California 94035, USA

  • *alejandro.perdomoortiz@nasa.gov

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Issue

Vol. 94, Iss. 2 — August 2016

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