Qubit Regularization and Qubit Embedding Algebras

TL;DR

This paper introduces qubit embedding algebras (QEAs) as a systematic way to understand the algebraic structures arising from qubit regularization in lattice quantum field theories, aiding quantum simulations.

Contribution

It presents a systematic method to derive QEAs for lattice models, revealing richer structures than previously known, and advancing the understanding of qubit regularization.

Findings

Derived QEAs for O(N) lattice spin models

Derived QEAs for SU(N) lattice gauge theories

Revealed richer algebraic structures than earlier approaches

Abstract

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 more richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.