Automatic structural search of tensor network states including entanglement renormalization

Watanabe, Ryo; Ueda, Hiroshi

Physical Review Research, 2024, 6(3), 033259

Number of Access:347（2025-09-12 06:38 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/98255

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Title
Automatic structural search of tensor network states including entanglement renormalization
Creator
CreatorName
Watanabe, Ryo
NRID
1000040632758 1000040632758
ORCID
0000-0001-9561-0933 0000-0001-9561-0933
researchmap permalink
hiroshi_ueda hiroshi_ueda
Scopus Author ID
57210940815 57210940815
CreatorName
Ueda, Hiroshi
Description
Watanabe R., Ueda H.. Automatic structural search of tensor network states including entanglement renormalization. Physical Review Research 6, 033259 (2024); https://doi.org/10.1103/PhysRevResearch.6.033259.
Abstract
Tensor network (TN) states, including entanglement renormalization (ER), can encompass a wider variety of entangled states. When the entanglement structure of the quantum state of interest is nonuniform in real space, accurately representing the state with a limited number of degrees of freedom hinges on appropriately configuring the TN to align with the entanglement pattern. However, a proposal has yet to show a structural search of ER due to its high computational cost and the lack of flexibility in its algorithm. In this study, we conducted an optimal structural search of TN, including ER, based on the reconstruction of their local structures with respect to variational energy. First, we demonstrated that our algorithm for the spin-1/2 tetramer singlets model could calculate exact ground energy using the multiscale entanglement renormalization ansatz (MERA) structure as an initial TN structure. Subsequently, we applied our algorithm to the random XY models with the two initial structures: MERA and the suitable structure underlying the strong disordered renormalization group. We found that, in both cases, our algorithm achieves improvements in variational energy, fidelity, and entanglement entropy. The degree of improvement in these quantities is superior in the latter case compared to the former, suggesting that utilizing an existing TN design method as a preprocessing step is important for maximizing our algorithm's performance.
Publisher
American Physical Society
Source Title
Physical Review Research
Volume (Issue)
6(3)
Page
033259
Date of Issued
2024-09-06
Language
English
Handle URL
https://hdl.handle.net/11094/98255
PISSN
26431564
Relation.isIdenticalTo
DOI (Publisher Version)
https://doi.org/10.1103/PhysRevResearch.6.033259
Access Rights
open access
CopyRight
This article is licensed under a Creative Commons Attribution 4.0 International License.
oaire:version
Version of Record
Category
学術雑誌論文 Journal Article