A diagrammatic approach to variational quantum ansatz construction

Variational quantum eigensolvers (VQEs) are a promising class of quantum algorithms for preparing approximate ground states in near-term quantum devices. Minimizing the error in such an approximation requires designing ansatzes using physical considerations that target the studied system. One such c...

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Autores principales:	Y. Herasymenko, T.E. O'Brien
Formato:	article
Lenguaje:	EN
Publicado:	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/409ee4310ddb466688e234218ee5069a
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spelling	oai:doaj.org-article:409ee4310ddb466688e234218ee5069a2021-12-02T16:23:26ZA diagrammatic approach to variational quantum ansatz construction2521-327X10.22331/q-2021-12-02-596https://doaj.org/article/409ee4310ddb466688e234218ee5069a2021-12-01T00:00:00Zhttps://quantum-journal.org/papers/q-2021-12-02-596/pdf/https://doaj.org/toc/2521-327XVariational quantum eigensolvers (VQEs) are a promising class of quantum algorithms for preparing approximate ground states in near-term quantum devices. Minimizing the error in such an approximation requires designing ansatzes using physical considerations that target the studied system. One such consideration is size-extensivity, meaning that the ground state quantum correlations are to be compactly represented in the ansatz. On digital quantum computers, however, the size-extensive ansatzes usually require expansion via Trotter-Suzuki methods. These introduce additional costs and errors to the approximation. In this work, we present a diagrammatic scheme for the digital VQE ansatzes, which is size-extensive but does not rely on Trotterization. We start by designing a family of digital ansatzes that explore the entire Hilbert space with the minimum number of free parameters. We then demonstrate how one may compress an arbitrary digital ansatz, by enforcing symmetry constraints of the target system, or by using them as parent ansatzes for a hierarchy of increasingly long but increasingly accurate sub-ansatzes. We apply a perturbative analysis and develop a diagrammatic formalism that ensures the size-extensivity of generated hierarchies. We test our methods on a short spin chain, finding good convergence to the ground state in the paramagnetic and the ferromagnetic phase of the transverse-field Ising model.Y. HerasymenkoT.E. O'BrienVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenarticlePhysicsQC1-999ENQuantum, Vol 5, p 596 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Y. Herasymenko T.E. O'Brien A diagrammatic approach to variational quantum ansatz construction
description	Variational quantum eigensolvers (VQEs) are a promising class of quantum algorithms for preparing approximate ground states in near-term quantum devices. Minimizing the error in such an approximation requires designing ansatzes using physical considerations that target the studied system. One such consideration is size-extensivity, meaning that the ground state quantum correlations are to be compactly represented in the ansatz. On digital quantum computers, however, the size-extensive ansatzes usually require expansion via Trotter-Suzuki methods. These introduce additional costs and errors to the approximation. In this work, we present a diagrammatic scheme for the digital VQE ansatzes, which is size-extensive but does not rely on Trotterization. We start by designing a family of digital ansatzes that explore the entire Hilbert space with the minimum number of free parameters. We then demonstrate how one may compress an arbitrary digital ansatz, by enforcing symmetry constraints of the target system, or by using them as parent ansatzes for a hierarchy of increasingly long but increasingly accurate sub-ansatzes. We apply a perturbative analysis and develop a diagrammatic formalism that ensures the size-extensivity of generated hierarchies. We test our methods on a short spin chain, finding good convergence to the ground state in the paramagnetic and the ferromagnetic phase of the transverse-field Ising model.
format	article
author	Y. Herasymenko T.E. O'Brien
author_facet	Y. Herasymenko T.E. O'Brien
author_sort	Y. Herasymenko
title	A diagrammatic approach to variational quantum ansatz construction
title_short	A diagrammatic approach to variational quantum ansatz construction
title_full	A diagrammatic approach to variational quantum ansatz construction
title_fullStr	A diagrammatic approach to variational quantum ansatz construction
title_full_unstemmed	A diagrammatic approach to variational quantum ansatz construction
title_sort	diagrammatic approach to variational quantum ansatz construction
publisher	Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
publishDate	2021
url	https://doaj.org/article/409ee4310ddb466688e234218ee5069a
work_keys_str_mv	AT yherasymenko adiagrammaticapproachtovariationalquantumansatzconstruction AT teobrien adiagrammaticapproachtovariationalquantumansatzconstruction AT yherasymenko diagrammaticapproachtovariationalquantumansatzconstruction AT teobrien diagrammaticapproachtovariationalquantumansatzconstruction
_version_	1718384105615261696

A diagrammatic approach to variational quantum ansatz construction

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