Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation

Abstract The imaginary-time evolution method is a well-known approach used for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of deep circuit depth and difficulty in the implementatio...

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Autores principales:	Hirofumi Nishi, Taichi Kosugi, Yu-ichiro Matsushita
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/2a1286c73f1745b082f552062a7cf304
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spelling	oai:doaj.org-article:2a1286c73f1745b082f552062a7cf3042021-12-02T18:25:06ZImplementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation10.1038/s41534-021-00409-y2056-6387https://doaj.org/article/2a1286c73f1745b082f552062a7cf3042021-06-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00409-yhttps://doaj.org/toc/2056-6387Abstract The imaginary-time evolution method is a well-known approach used for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of deep circuit depth and difficulty in the implementation on noisy intermediate-scale quantum (NISQ) devices. In this study, a nonlocal approximation is developed to tackle this difficulty. We found that by removing the locality condition or local approximation (LA), which was imposed when the imaginary-time evolution operator is converted to a unitary operator, the quantum circuit depth is significantly reduced. We propose two-step approximation methods based on a nonlocality condition: extended LA (eLA) and nonlocal approximation (NLA). To confirm the validity of eLA and NLA, we apply them to the max-cut problem of an unweighted 3-regular graph and a weighted fully connected graph; we comparatively evaluate the performances of LA, eLA, and NLA. The eLA and NLA methods require far fewer circuit depths than LA to maintain the same level of computational accuracy. Further, we developed a “compression” method of the quantum circuit for the imaginary-time steps to further reduce the circuit depth in the QITE method. The eLA, NLA, and compression methods introduced in this study allow us to reduce the circuit depth and the accumulation of error caused by the gate operation significantly and pave the way for implementing the QITE method on NISQ devices.Hirofumi NishiTaichi KosugiYu-ichiro MatsushitaNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-7 (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 Hirofumi Nishi Taichi Kosugi Yu-ichiro Matsushita Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation
description	Abstract The imaginary-time evolution method is a well-known approach used for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of deep circuit depth and difficulty in the implementation on noisy intermediate-scale quantum (NISQ) devices. In this study, a nonlocal approximation is developed to tackle this difficulty. We found that by removing the locality condition or local approximation (LA), which was imposed when the imaginary-time evolution operator is converted to a unitary operator, the quantum circuit depth is significantly reduced. We propose two-step approximation methods based on a nonlocality condition: extended LA (eLA) and nonlocal approximation (NLA). To confirm the validity of eLA and NLA, we apply them to the max-cut problem of an unweighted 3-regular graph and a weighted fully connected graph; we comparatively evaluate the performances of LA, eLA, and NLA. The eLA and NLA methods require far fewer circuit depths than LA to maintain the same level of computational accuracy. Further, we developed a “compression” method of the quantum circuit for the imaginary-time steps to further reduce the circuit depth in the QITE method. The eLA, NLA, and compression methods introduced in this study allow us to reduce the circuit depth and the accumulation of error caused by the gate operation significantly and pave the way for implementing the QITE method on NISQ devices.
format	article
author	Hirofumi Nishi Taichi Kosugi Yu-ichiro Matsushita
author_facet	Hirofumi Nishi Taichi Kosugi Yu-ichiro Matsushita
author_sort	Hirofumi Nishi
title	Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation
title_short	Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation
title_full	Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation
title_fullStr	Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation
title_full_unstemmed	Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation
title_sort	implementation of quantum imaginary-time evolution method on nisq devices by introducing nonlocal approximation
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/2a1286c73f1745b082f552062a7cf304
work_keys_str_mv	AT hirofuminishi implementationofquantumimaginarytimeevolutionmethodonnisqdevicesbyintroducingnonlocalapproximation AT taichikosugi implementationofquantumimaginarytimeevolutionmethodonnisqdevicesbyintroducingnonlocalapproximation AT yuichiromatsushita implementationofquantumimaginarytimeevolutionmethodonnisqdevicesbyintroducingnonlocalapproximation
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Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation

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