Quantum algorithms for Monte Carlo integration using pseudo-random numbers

Miyamoto, Koichi

doi:10.1109/qce52317.2021.00075

2021 IEEE International Conference on Quantum Computing and Engineering (QCE) 2021

DOI: 10.1109/qce52317.2021.00075

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Quantum algorithms for Monte Carlo integration using pseudo-random numbers

Koichi Miyamoto

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2024

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A general quantum algorithm for numerical integration

Shu,

Shan,

et al. 2024

Sci Rep

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Quantum algorithms have shown their superiority in many application fields. However, a general quantum algorithm for numerical integration, an indispensable tool for processing sophisticated science and engineering issues, is still missing. Here, we first proposed a quantum integration algorithm suitable for any continuous functions that can be approximated by polynomials. More impressively, the algorithm achieves quantum encoding of any integrable functions through polynomial approximation, then constructs a quantum oracle to mark the number of points in the integration area and finally converts the statistical results into the phase angle in the amplitude of the superposition state. The quantum algorithm introduced in this work exhibits quadratic acceleration over the classical integration algorithms by reducing computational complexity from O(N) to O(√N). Our work addresses the crucial impediments for improving the generality of quantum integration algorithm, which provides a meaningful guidance for expanding the superiority of quantum computing.

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A general quantum algorithm for numerical integration

Shu,

Shan,

et al. 2024

Sci Rep

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

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Quantum algorithms for Monte Carlo integration using pseudo-random numbers

Cited by 1 publication

References 57 publications

A general quantum algorithm for numerical integration

A general quantum algorithm for numerical integration

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