Quantum inference on Bayesian networks
Name
PhysRevA.89.062315.pdf
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442.27 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Low, Guang Hao
Yoder, Theodore James
Chuang, Isaac L.
Date Issued
June 2014
Journal
Physical Review A
Publisher
American Physical Society
Citation
Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. “Quantum Inference on Bayesian Networks.” Phys. Rev. A 89, no. 6 (June 2014). © 2014 American Physical Society
Version
Final published version
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)[superscript −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(n2[superscript m]P(e)[superscript −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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.89.062315
