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Cited by 109Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyBayesian Modeling and Causal Inference

Quantum inference on Bayesian networks

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Low, Guang Hao, Yoder, Theodore J., Chuang, Isaac L.·2014·Physical Review A
DOI 10.1103/physreva.89.062315
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Abstract

Performing exact inference on Bayesian networks is known to be $#P$-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically, a single unbiased sample is obtained from a Bayesian network on $n$ variables with at most $m$ parents per node in time $O(nmP{(e)}^{\ensuremath{-}1})$, depending critically on $P(e)$, the probability that the evidence might occur in the first place. By implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking $O(n{2}^{m}P{(e)}^{\ensuremath{-}\frac{1}{2}})$ time per sample. We exploit the Bayesian network's graph structure to efficiently construct a quantum state, a q-sample, representing the intended classical distribution, and also to efficiently apply amplitude amplification, the source of our speedup. Thus, our speedup is notable as it is unrelativized---we count primitive operations and require no blackbox oracle queries.

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  • Sufficiently powerful quantum computers can in principle provide computational speedups for key machine learning algorithms and subroutines such as data fitting, principal component analysis, Bayesian inference, Monte Carlo methods, support vector machines, Boltzmann machines, and recommendation systems.

    “Sufficiently powerful quantum computers can in principle provide computational speedups for key machine learning algorithms and subroutines such as data fitting [4], principal component analysis [5], Bayesian inference [6,7], Monte Carlo methods [8], support vector machines [9,10], Boltzmann machines [11,12], and recommendation systems [13].”

    From Continuous-variable quantum neural networks (2019) · cites this paper as [6]

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Authors
Low, G. H., Yoder, T. J., & Chuang, I. L.
Affiliations
Massachusetts Institute of Technology (US)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2014-06-13
Volume
89
Issue
6
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.89.062315
OpenAlex
W1559984405
Cited by
109
References
42
Citations by year
2026: 4 · 2025: 16 · 2024: 11 · 2023: 18 · 2022: 14 · 2021: 15 · 2020: 10 · 2019: 8 · 2018: 7 · 2017: 3 · 2016: 3
FWCI
1.99
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
  • arXiv (Cornell University)
  • Physical Review Letters
Funders
  • National Science Foundation
  • Army Research Office
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
Keywords
Bayesian networks, amplitude amplification, approximate inference, quantum advantage, #P-hardness, sampling from distributions

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