A Geometric View on Quantum Tensor Networks

A Geometric View on Quantum Tensor Networks

Tensor network states and algorithms play a key role in understanding the structure of complex quantum systems and their entanglement properties. This report is devoted to the problem of the construction of an arbitrary quantum state using the differential geometric scheme of covariant series in Rie...

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Main Author: Tsirulev Alexander
Format: Article
Language:English
Published: EDP Sciences 2020-01-01
Series:EPJ Web of Conferences
Online Access:https://www.epj-conferences.org/articles/epjconf/pdf/2020/02/epjconf_mmcp2019_02022.pdf
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spelling doaj-7049a2aadbd44b81bafbf7a36678985d2021-08-02T14:19:04ZengEDP SciencesEPJ Web of Conferences2100-014X2020-01-012260202210.1051/epjconf/202022602022epjconf_mmcp2019_02022A Geometric View on Quantum Tensor NetworksTsirulev AlexanderTensor network states and algorithms play a key role in understanding the structure of complex quantum systems and their entanglement properties. This report is devoted to the problem of the construction of an arbitrary quantum state using the differential geometric scheme of covariant series in Riemann normal coordinates. The building blocks of the scheme are polynomials in the Pauli operators with the coefficients specified by the curvature, torsion, and their covariant derivatives on some base manifold. The problem of measuring the entanglement of multipartite mixed states is shortly discussed.https://www.epj-conferences.org/articles/epjconf/pdf/2020/02/epjconf_mmcp2019_02022.pdf
collection DOAJ
language English
format Article
sources DOAJ
author Tsirulev Alexander
spellingShingle Tsirulev Alexander
A Geometric View on Quantum Tensor Networks
EPJ Web of Conferences
author_facet Tsirulev Alexander
author_sort Tsirulev Alexander
title A Geometric View on Quantum Tensor Networks
title_short A Geometric View on Quantum Tensor Networks
title_full A Geometric View on Quantum Tensor Networks
title_fullStr A Geometric View on Quantum Tensor Networks
title_full_unstemmed A Geometric View on Quantum Tensor Networks
title_sort geometric view on quantum tensor networks
publisher EDP Sciences
series EPJ Web of Conferences
issn 2100-014X
publishDate 2020-01-01
description Tensor network states and algorithms play a key role in understanding the structure of complex quantum systems and their entanglement properties. This report is devoted to the problem of the construction of an arbitrary quantum state using the differential geometric scheme of covariant series in Riemann normal coordinates. The building blocks of the scheme are polynomials in the Pauli operators with the coefficients specified by the curvature, torsion, and their covariant derivatives on some base manifold. The problem of measuring the entanglement of multipartite mixed states is shortly discussed.
url https://www.epj-conferences.org/articles/epjconf/pdf/2020/02/epjconf_mmcp2019_02022.pdf
work_keys_str_mv AT tsirulevalexander ageometricviewonquantumtensornetworks
AT tsirulevalexander geometricviewonquantumtensornetworks
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