Quantum simulation of lattice gauge theories coupled to fermionic matter via anyonic regularization

TL;DR

This paper introduces a novel regularization method for lattice gauge theories using anyonic models derived from Chern-Simons theory, enabling quantum simulation of gauge fields coupled to fermions.

Contribution

It develops a framework to regularize gauge fields with braided fusion categories and couples them to fermionic matter via fusion surface models, with explicit quantum circuit implementations.

Findings

Regularization of gauge fields using braided fusion categories.

Coupling of regularized gauge theories to fermionic matter as anyons.

Quantum circuit constructions for simulating the models on fault-tolerant quantum computers.

Abstract

The optimal regularization of infinite-dimensional degrees of freedom is a central open problem in the tractable simulation of lattice gauge theories on quantum computers. Here, we consider regularizing the gauge field by replacing the gauge group $G$ with a braided fusion category whose objects correspond to Wilson lines of the associated Chern-Simons theory $G_k$, with the level $k$ serving as the regularization parameter. We demonstrate how to couple these regularized $U(1)$ and $SU(2)$ gauge groups to fermionic matter using the framework of fusion surface models, which treats matter and gauge field excitations as interacting anyons. We then address the simulation of the Hamiltonians we construct on fault-tolerant quantum computers, providing explicit quantum circuit constructions for implementing the primitive gates in this model, namely, the $F$ and $R$ symbols of the $U(1)_k$ and $SU(2)_k$ anyon theories, which may be of independent interest.