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The Quantum Complexity of Markov Chain Monte Carlo

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Logic and Theory of Algorithms (CiE 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5028))

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Abstract

Markov chain Monte Carlo (MCMC) is the widely-used classical method of random sampling from a probability distribution π by simulating a Markov chain which “mixes” to π at equilibrium. Despite the success quantum walks have been shown to have in speeding up random walk algorithms for search problems (“hitting”) and simulated annealing, it remains to prove a general speedup theorem for MCMC sampling algorithms. We review the progress toward this end, in particular using decoherent quantum walks.

This material is based upon work supported by the National Science Foundation under Grant No. 0523866 and is adapted in part from the author’s PhD thesis at Rutgers University [1].

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Authors and Affiliations

  1. Laboratoire de Recherche en Informatique, Université de Paris-Sud XI, 91405, Orsay, France

    Peter C. Richter

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  1. Peter C. Richter
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Arnold Beckmann Costas Dimitracopoulos Benedikt Löwe

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Richter, P.C. (2008). The Quantum Complexity of Markov Chain Monte Carlo. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_55

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  • DOI: https://doi.org/10.1007/978-3-540-69407-6_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69405-2

  • Online ISBN: 978-3-540-69407-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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