The DOI matches its Crossref record; 51 of the 51 references it cites were found in a registry or an index.
Quantum speedup of Monte Carlo methods
Open accessAbstract
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 randomized 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.
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Cites
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 18,842
Quantum Mechanics Helps in Searching for a Needle in a Haystack
Grover, L. K. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.325 · Cited by 4,306
Monte Carlo Methods in Financial Engineering
Glasserman, P. (2003) · Stochastic Modelling and Applied Probability · doi:10.1007/978-0-387-21617-1 · Cited by 3,782
Markov Chains and Mixing Times
Levin, D., Peres, Y., & Wilmer, E. (2008) · doi:10.1090/mbk/058 · Cited by 2,241
Quantum amplitude amplification and estimation
Brassard, G., Høyer, P., Mosca, M., & Tapp, A. (2002) · Contemporary Mathematics · doi:10.1090/conm/305/05215 · Cited by 1,680
Strengths and Weaknesses of Quantum Computing
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The Monte Carlo Method for Semiconductor Device Simulation
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Quantum walks: a comprehensive review
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Cited by
Quantum computing for finance: Overview and prospects
Orús, R., Mugel, S., & Lizaso, E. (2019) · Reviews in Physics · doi:10.1016/j.revip.2019.100028 · Cited by 668
Continuous-variable quantum neural networks
Killoran, N., Bromley, T. R., Arrazola, J. M., Schuld, M., Quesada, N., & Lloyd, S. (2019) · Physical Review Research · doi:10.1103/physrevresearch.1.033063 · Cited by 418
Focus beyond Quadratic Speedups for Error-Corrected Quantum Advantage
Babbush, R., McClean, J. R., Newman, M., Gidney, C., Boixo, S., & Neven, H. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010103 · Cited by 148
Biology and medicine in the landscape of quantum advantages
Cordier, B. A., Sawaya, N. P. D., Guerreschi, G. G., & McWeeney, S. K. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0541 · Cited by 87
Minimizing Estimation Runtime on Noisy Quantum Computers
Wang, G., Koh, D. E., Johnson, P. D., & Cao, Y. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010346 · Cited by 77
Metadata
- Authors
- Montanaro, A.
- Venue
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 2015-09
- Volume
- 471
- Issue
- 2181
- Pages
- 20150301
- ISSN
- 1364-5021 (ISSN-L)
- 1471-2946
- OpenAlex
- W2164248509
- Cited by
- 334
- References
- 51
- FWCI
- 4.38
- Type
- journal article
- Language
- en
- Open access
- hybrid
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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