Reduction of the molecular hamiltonian matrix using quantum community detection

Abstract Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires ap...

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Autores principales:	Susan M. Mniszewski, Pavel A. Dub, Sergei Tretiak, Petr M. Anisimov, Yu Zhang, Christian F. A. Negre
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/3dd9b6f2d0cb44f4a3ca79bf22e2b6fc
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spelling	oai:doaj.org-article:3dd9b6f2d0cb44f4a3ca79bf22e2b6fc2021-12-02T14:04:00ZReduction of the molecular hamiltonian matrix using quantum community detection10.1038/s41598-021-83561-x2045-2322https://doaj.org/article/3dd9b6f2d0cb44f4a3ca79bf22e2b6fc2021-02-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-83561-xhttps://doaj.org/toc/2045-2322Abstract Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.Susan M. MniszewskiPavel A. DubSergei TretiakPetr M. AnisimovYu ZhangChristian F. A. NegreNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-13 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Susan M. Mniszewski Pavel A. Dub Sergei Tretiak Petr M. Anisimov Yu Zhang Christian F. A. Negre Reduction of the molecular hamiltonian matrix using quantum community detection
description	Abstract Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.
format	article
author	Susan M. Mniszewski Pavel A. Dub Sergei Tretiak Petr M. Anisimov Yu Zhang Christian F. A. Negre
author_facet	Susan M. Mniszewski Pavel A. Dub Sergei Tretiak Petr M. Anisimov Yu Zhang Christian F. A. Negre
author_sort	Susan M. Mniszewski
title	Reduction of the molecular hamiltonian matrix using quantum community detection
title_short	Reduction of the molecular hamiltonian matrix using quantum community detection
title_full	Reduction of the molecular hamiltonian matrix using quantum community detection
title_fullStr	Reduction of the molecular hamiltonian matrix using quantum community detection
title_full_unstemmed	Reduction of the molecular hamiltonian matrix using quantum community detection
title_sort	reduction of the molecular hamiltonian matrix using quantum community detection
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/3dd9b6f2d0cb44f4a3ca79bf22e2b6fc
work_keys_str_mv	AT susanmmniszewski reductionofthemolecularhamiltonianmatrixusingquantumcommunitydetection AT paveladub reductionofthemolecularhamiltonianmatrixusingquantumcommunitydetection AT sergeitretiak reductionofthemolecularhamiltonianmatrixusingquantumcommunitydetection AT petrmanisimov reductionofthemolecularhamiltonianmatrixusingquantumcommunitydetection AT yuzhang reductionofthemolecularhamiltonianmatrixusingquantumcommunitydetection AT christianfanegre reductionofthemolecularhamiltonianmatrixusingquantumcommunitydetection
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Reduction of the molecular hamiltonian matrix using quantum community detection

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