Hamiltonian simulation in the low-energy subspace

Abstract We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian H. This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the l...

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Autores principales:	Burak Şahinoğlu, Rolando D. Somma
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/0abb0e983c9f48f5aa8ef9d679deeb4c
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id	oai:doaj.org-article:0abb0e983c9f48f5aa8ef9d679deeb4c
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spelling	oai:doaj.org-article:0abb0e983c9f48f5aa8ef9d679deeb4c2021-12-02T18:46:59ZHamiltonian simulation in the low-energy subspace10.1038/s41534-021-00451-w2056-6387https://doaj.org/article/0abb0e983c9f48f5aa8ef9d679deeb4c2021-07-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00451-whttps://doaj.org/toc/2056-6387Abstract We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian H. This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the low-energy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective low-energy norm of H. We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove exponentially decaying upper bounds on the leakage to high-energy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality.Burak ŞahinoğluRolando D. SommaNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-5 (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 Burak Şahinoğlu Rolando D. Somma Hamiltonian simulation in the low-energy subspace
description	Abstract We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian H. This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the low-energy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective low-energy norm of H. We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove exponentially decaying upper bounds on the leakage to high-energy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality.
format	article
author	Burak Şahinoğlu Rolando D. Somma
author_facet	Burak Şahinoğlu Rolando D. Somma
author_sort	Burak Şahinoğlu
title	Hamiltonian simulation in the low-energy subspace
title_short	Hamiltonian simulation in the low-energy subspace
title_full	Hamiltonian simulation in the low-energy subspace
title_fullStr	Hamiltonian simulation in the low-energy subspace
title_full_unstemmed	Hamiltonian simulation in the low-energy subspace
title_sort	hamiltonian simulation in the low-energy subspace
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/0abb0e983c9f48f5aa8ef9d679deeb4c
work_keys_str_mv	AT buraksahinoglu hamiltoniansimulationinthelowenergysubspace AT rolandodsomma hamiltoniansimulationinthelowenergysubspace
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Hamiltonian simulation in the low-energy subspace

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