Qubit Regularization and Qubit Embedding Algebras

Journal Article · 01 February 2022 · Symmetry

DOI: https://doi.org/10.3390/sym14020305 · OSTI ID:1843898

Liu, Hanqing ; Chandrasekharan, Shailesh

Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the O(N) lattice spin models and the SU(N) lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.

• Sponsoring Organization: USDOE
• Grant/Contract Number: FG02-05ER41368; 89233218CNA000001
• OSTI ID: 1843898
• Journal Information: Symmetry, Journal Name: Symmetry Journal Issue: 2 Vol. 14; ISSN SYMMAM; ISSN 2073-8994
• Publisher: MDPI AGCopyright Statement
• Country of Publication: Switzerland
• Language: English