Quantum-enhanced analysis of discrete stochastic processes

Abstract Discrete stochastic processes (DSP) are instrumental for modeling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte-Carlo methods since the number of realizations increases exponentially with the nu...

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Autores principales:	Carsten Blank, Daniel K. Park, Francesco Petruccione
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/70ee040d9b934c0c89b96c9c4ff0fd91
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spelling	oai:doaj.org-article:70ee040d9b934c0c89b96c9c4ff0fd912021-12-02T19:06:44ZQuantum-enhanced analysis of discrete stochastic processes10.1038/s41534-021-00459-22056-6387https://doaj.org/article/70ee040d9b934c0c89b96c9c4ff0fd912021-08-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00459-2https://doaj.org/toc/2056-6387Abstract Discrete stochastic processes (DSP) are instrumental for modeling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte-Carlo methods since the number of realizations increases exponentially with the number of time steps, and importance sampling is often required to reduce the variance. We propose a quantum algorithm for calculating the characteristic function of a DSP, which completely defines its probability distribution, using the number of quantum circuit elements that grows only linearly with the number of time steps. The quantum algorithm reduces the Monte-Carlo sampling to a Bernoulli trial while taking all stochastic trajectories into account. This approach guarantees the optimal variance without the need for importance sampling. The algorithm can be further furnished with the quantum amplitude estimation algorithm to provide quadratic speed-up in sampling. The Fourier approximation can be used to estimate an expectation value of any integrable function of the random variable. Applications in finance and correlated random walks are presented. Proof-of-principle experiments are performed using the IBM quantum cloud platform.Carsten BlankDaniel K. ParkFrancesco PetruccioneNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
spellingShingle	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 Carsten Blank Daniel K. Park Francesco Petruccione Quantum-enhanced analysis of discrete stochastic processes
description	Abstract Discrete stochastic processes (DSP) are instrumental for modeling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte-Carlo methods since the number of realizations increases exponentially with the number of time steps, and importance sampling is often required to reduce the variance. We propose a quantum algorithm for calculating the characteristic function of a DSP, which completely defines its probability distribution, using the number of quantum circuit elements that grows only linearly with the number of time steps. The quantum algorithm reduces the Monte-Carlo sampling to a Bernoulli trial while taking all stochastic trajectories into account. This approach guarantees the optimal variance without the need for importance sampling. The algorithm can be further furnished with the quantum amplitude estimation algorithm to provide quadratic speed-up in sampling. The Fourier approximation can be used to estimate an expectation value of any integrable function of the random variable. Applications in finance and correlated random walks are presented. Proof-of-principle experiments are performed using the IBM quantum cloud platform.
format	article
author	Carsten Blank Daniel K. Park Francesco Petruccione
author_facet	Carsten Blank Daniel K. Park Francesco Petruccione
author_sort	Carsten Blank
title	Quantum-enhanced analysis of discrete stochastic processes
title_short	Quantum-enhanced analysis of discrete stochastic processes
title_full	Quantum-enhanced analysis of discrete stochastic processes
title_fullStr	Quantum-enhanced analysis of discrete stochastic processes
title_full_unstemmed	Quantum-enhanced analysis of discrete stochastic processes
title_sort	quantum-enhanced analysis of discrete stochastic processes
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/70ee040d9b934c0c89b96c9c4ff0fd91
work_keys_str_mv	AT carstenblank quantumenhancedanalysisofdiscretestochasticprocesses AT danielkpark quantumenhancedanalysisofdiscretestochasticprocesses AT francescopetruccione quantumenhancedanalysisofdiscretestochasticprocesses
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Quantum-enhanced analysis of discrete stochastic processes

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