Quantum speedup of Monte Carlo methods

A. Montanaro · 2015 · Proc. R. Soc. A 471, 20150301

| 编号 QC023 | 主题 量子算法工具箱 | 链接 arXiv:1504.06987 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomised or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

本站词条在引用该文献时，会以 wikilink（sources/QC023）链接到本页；右侧「反向链接」面板自动列出所有引用它的词条。