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Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning
Open accessAbstract
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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“Quantum algorithms have been proposed, using a D-Wave machine [101-103] or a circuit algorithm [104]; that sample from the Boltzmann distribution quadratically faster than it is possible classically [23].”
From The prospects of quantum computing in computational molecular biology (2021) · cites this paper as [103]
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Metadata
- Authors
- Benedetti, M., Realpe-Gómez, J., Biswas, R., & Perdomo-Ortiz, A.
- Affiliations
- Ames Research Center (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2016-08-09
- Volume
- 94
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2517233404
- Cited by
- 215
- References
- 57
- Citations by year
- 2026: 15 · 2025: 17 · 2024: 14 · 2023: 27 · 2022: 27 · 2021: 18 · 2020: 23 · 2019: 27 · 2018: 29 · 2017: 13 · 2016: 5
- FWCI
- 20.06
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Ames Research Center (NNA14AA60C, NAS2-03144)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum annealers, effective temperature estimation, Boltzmann sampling, restricted Boltzmann machine, quantum machine learning, contrastive divergence, deep learning, quantum computing hardware, sampling efficiency
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