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Title: Tensor lattice field theory with applications to the renormalization group and quantum computing

Abstract

We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these lattice models can be reformulated using tensorial methods where the field integrations in the path-integral formalism are replaced by discrete sums. These formulations involve various types of duality and provide exact coarse-graining formulas which can be combined with truncations to obtain practical implementations of the Wilson renormalization group program. Tensor reformulations are naturally discrete and provide manageable transfer matrices. Combining truncations with the time continuum limit, we derive Hamiltonians suitable to perform quantum simulation experiments, for instance using cold atoms, or to be programmed on existing quantum computers. We review recent progress concerning the tensor field theory treatment of non-compact scalar models, supersymmetric models, economical four-dimensional algorithms, noise-robust enforcement of Gauss's law, symmetry preserving truncations and topological considerations. We discuss connections with other tensor network approaches.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]
  1. Iowa U.
  2. Syracuse U.; Fermilab
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1831959
Report Number(s):
FERMILAB-PUB-20-580-QIS-T; arXiv:2010.06539
oai:inspirehep.net:1822435
DOE Contract Number:  
AC02-07CH11359
Resource Type:
Journal Article
Journal Name:
TBD
Additional Journal Information:
Journal Name: TBD
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Meurice, Yannick, Sakai, Ryo, and Unmuth-Yockey, Judah. Tensor lattice field theory with applications to the renormalization group and quantum computing. United States: N. p., 2020. Web.
Meurice, Yannick, Sakai, Ryo, & Unmuth-Yockey, Judah. Tensor lattice field theory with applications to the renormalization group and quantum computing. United States.
Meurice, Yannick, Sakai, Ryo, and Unmuth-Yockey, Judah. 2020. "Tensor lattice field theory with applications to the renormalization group and quantum computing". United States. https://www.osti.gov/servlets/purl/1831959.
@article{osti_1831959,
title = {Tensor lattice field theory with applications to the renormalization group and quantum computing},
author = {Meurice, Yannick and Sakai, Ryo and Unmuth-Yockey, Judah},
abstractNote = {We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these lattice models can be reformulated using tensorial methods where the field integrations in the path-integral formalism are replaced by discrete sums. These formulations involve various types of duality and provide exact coarse-graining formulas which can be combined with truncations to obtain practical implementations of the Wilson renormalization group program. Tensor reformulations are naturally discrete and provide manageable transfer matrices. Combining truncations with the time continuum limit, we derive Hamiltonians suitable to perform quantum simulation experiments, for instance using cold atoms, or to be programmed on existing quantum computers. We review recent progress concerning the tensor field theory treatment of non-compact scalar models, supersymmetric models, economical four-dimensional algorithms, noise-robust enforcement of Gauss's law, symmetry preserving truncations and topological considerations. We discuss connections with other tensor network approaches.},
doi = {},
url = {https://www.osti.gov/biblio/1831959}, journal = {TBD},
number = ,
volume = ,
place = {United States},
year = {Tue Oct 13 00:00:00 EDT 2020},
month = {Tue Oct 13 00:00:00 EDT 2020}
}