Low rank representations for quantum simulation of electronic structure

Abstract The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $${\mathcal{O}}({N}^{4})$$ O ( N 4 ) gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primiti...

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Autores principales:	Mario Motta, Erika Ye, Jarrod R. McClean, Zhendong Li, Austin J. Minnich, Ryan Babbush, Garnet Kin-Lic Chan
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/952d283f874a4287ae1b8234c4cc470a
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spelling	oai:doaj.org-article:952d283f874a4287ae1b8234c4cc470a2021-12-02T14:47:39ZLow rank representations for quantum simulation of electronic structure10.1038/s41534-021-00416-z2056-6387https://doaj.org/article/952d283f874a4287ae1b8234c4cc470a2021-05-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00416-zhttps://doaj.org/toc/2056-6387Abstract The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $${\mathcal{O}}({N}^{4})$$ O ( N 4 ) gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) gate complexity in small simulations, which reduces to $${\mathcal{O}}({N}^{2})$$ O ( N 2 ) gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have $${\mathcal{O}}({N}^{2})$$ O ( N 2 ) depth on a linearly connected array, an improvement over the $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 105 non-Clifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes.Mario MottaErika YeJarrod R. McCleanZhendong LiAustin J. MinnichRyan BabbushGarnet Kin-Lic ChanNature 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 Mario Motta Erika Ye Jarrod R. McClean Zhendong Li Austin J. Minnich Ryan Babbush Garnet Kin-Lic Chan Low rank representations for quantum simulation of electronic structure
description	Abstract The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the $${\mathcal{O}}({N}^{4})$$ O ( N 4 ) gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) gate complexity in small simulations, which reduces to $${\mathcal{O}}({N}^{2})$$ O ( N 2 ) gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have $${\mathcal{O}}({N}^{2})$$ O ( N 2 ) depth on a linearly connected array, an improvement over the $${\mathcal{O}}({N}^{3})$$ O ( N 3 ) scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 105 non-Clifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes.
format	article
author	Mario Motta Erika Ye Jarrod R. McClean Zhendong Li Austin J. Minnich Ryan Babbush Garnet Kin-Lic Chan
author_facet	Mario Motta Erika Ye Jarrod R. McClean Zhendong Li Austin J. Minnich Ryan Babbush Garnet Kin-Lic Chan
author_sort	Mario Motta
title	Low rank representations for quantum simulation of electronic structure
title_short	Low rank representations for quantum simulation of electronic structure
title_full	Low rank representations for quantum simulation of electronic structure
title_fullStr	Low rank representations for quantum simulation of electronic structure
title_full_unstemmed	Low rank representations for quantum simulation of electronic structure
title_sort	low rank representations for quantum simulation of electronic structure
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/952d283f874a4287ae1b8234c4cc470a
work_keys_str_mv	AT mariomotta lowrankrepresentationsforquantumsimulationofelectronicstructure AT erikaye lowrankrepresentationsforquantumsimulationofelectronicstructure AT jarrodrmcclean lowrankrepresentationsforquantumsimulationofelectronicstructure AT zhendongli lowrankrepresentationsforquantumsimulationofelectronicstructure AT austinjminnich lowrankrepresentationsforquantumsimulationofelectronicstructure AT ryanbabbush lowrankrepresentationsforquantumsimulationofelectronicstructure AT garnetkinlicchan lowrankrepresentationsforquantumsimulationofelectronicstructure
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Low rank representations for quantum simulation of electronic structure

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