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Despite the attempts to apply a quantum annealer to Boltzmann sampling, it is still impossible to perform accurate sampling at arbitrary temperatures. Conventional distribution correction methods such as importance sampling and resampling cannot be applied, because the analytical expression of sampling distribution is unknown for a quantum annealer. Stein correction (Liu and Lee, 2017) can correct the samples by weighting without the knowledge of the sampling distribution, but the naive implementation requires the solution of a large-scale quadratic program, hampering usage in practical problems. In this letter, a fast and approximate method based on random feature map and exponentiated gradient updates is developed to compute the sample weights, and used to correct the samples generated by D-Wave quantum annealers. In benchmarking problems, it is observed that the residual error of thermal average calculations is reduced significantly. If combined with our method, quantum annealers may emerge as a viable alternative to long-established Markov chain Monte Carlo methods.

Rights:

• Creative Commons BY Attribution 4.0 International
  

Keyword: Boltzmann sampling, quantum annealer

Date published: 2024-10-21

Publisher: American Physical Society (APS)

Journal:

• Physical Review Research (ISSN: 26431564) vol. 6 issue. 4 043050

Funding:

• Japan Science and Technology Agency JPMJCR21U2
• Core Research for Evolutional Science and Technology JPMJCR21O2
• Exploratory Research for Advanced Technology JPMJER1903
• Ministry of Education, Culture, Sports, Science and Technology JPMXP1122712807
• Japan Society for the Promotion of Science 19H05819

Manuscript type: Publisher's version (Version of record)

MDR DOI:

First published URL: https://doi.org/10.1103/physrevresearch.6.043050

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Updated at: 2024-10-25 16:30:56 +0900

Published on MDR: 2024-10-25 16:30:56 +0900