Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics

We present a novel, nonparametric form for compactly representing entangled many-body quantum states, which we call a “Gaussian process state.” In contrast to other approaches, we define this state explicitly in terms of a configurational data set, with the probability amplitudes statistically infer...

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Autores principales:	Aldo Glielmo, Yannic Rath, Gábor Csányi, Alessandro De Vita, George H. Booth
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/f1450e7affce407e84c56dbc21f15663
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spelling	oai:doaj.org-article:f1450e7affce407e84c56dbc21f156632021-12-02T12:43:11ZGaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics10.1103/PhysRevX.10.0410262160-3308https://doaj.org/article/f1450e7affce407e84c56dbc21f156632020-11-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.041026http://doi.org/10.1103/PhysRevX.10.041026https://doaj.org/toc/2160-3308We present a novel, nonparametric form for compactly representing entangled many-body quantum states, which we call a “Gaussian process state.” In contrast to other approaches, we define this state explicitly in terms of a configurational data set, with the probability amplitudes statistically inferred from this data according to Bayesian statistics. In this way, the nonlocal physical correlated features of the state can be analytically resummed, allowing for exponential complexity to underpin the ansatz, but efficiently represented in a small data set. The state is found to be highly compact, systematically improvable, and efficient to sample, representing a large number of known variational states within its span. It is also proven to be a “universal approximator” for quantum states, able to capture any entangled many-body state with increasing data-set size. We develop two numerical approaches which can learn this form directly—a fragmentation approach and direct variational optimization—and apply these schemes to the fermionic Hubbard model. We find competitive or superior descriptions of correlated quantum problems compared to existing state-of-the-art variational ansatzes, as well as other numerical methods.Aldo GlielmoYannic RathGábor CsányiAlessandro De VitaGeorge H. BoothAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 4, p 041026 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Aldo Glielmo Yannic Rath Gábor Csányi Alessandro De Vita George H. Booth Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics
description	We present a novel, nonparametric form for compactly representing entangled many-body quantum states, which we call a “Gaussian process state.” In contrast to other approaches, we define this state explicitly in terms of a configurational data set, with the probability amplitudes statistically inferred from this data according to Bayesian statistics. In this way, the nonlocal physical correlated features of the state can be analytically resummed, allowing for exponential complexity to underpin the ansatz, but efficiently represented in a small data set. The state is found to be highly compact, systematically improvable, and efficient to sample, representing a large number of known variational states within its span. It is also proven to be a “universal approximator” for quantum states, able to capture any entangled many-body state with increasing data-set size. We develop two numerical approaches which can learn this form directly—a fragmentation approach and direct variational optimization—and apply these schemes to the fermionic Hubbard model. We find competitive or superior descriptions of correlated quantum problems compared to existing state-of-the-art variational ansatzes, as well as other numerical methods.
format	article
author	Aldo Glielmo Yannic Rath Gábor Csányi Alessandro De Vita George H. Booth
author_facet	Aldo Glielmo Yannic Rath Gábor Csányi Alessandro De Vita George H. Booth
author_sort	Aldo Glielmo
title	Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics
title_short	Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics
title_full	Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics
title_fullStr	Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics
title_full_unstemmed	Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics
title_sort	gaussian process states: a data-driven representation of quantum many-body physics
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/f1450e7affce407e84c56dbc21f15663
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Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics

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