A Formulation of Lattice Gauge Theories for Quantum Simulations

TL;DR

This paper reformulates lattice gauge theories using fermionic and bosonic degrees of freedom to facilitate quantum simulation, addressing both discrete and continuous gauge groups with practical truncation schemes.

Contribution

It introduces a Fock space-based Hamiltonian formulation for lattice gauge theories suitable for quantum simulators, including methods for truncating continuous groups and connecting to topological models.

Findings

Provides a Fock space formulation of gauge theories.

Develops a truncation scheme for continuous gauge groups.

Connects lattice gauge theories to topological quantum models.

Abstract

We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We consider both discrete and continuous gauge groups and adopt a realistic multi-component Fock space for the definition of matter degrees of freedom. In particular, we express the Hamiltonian of the gauge theory and the Gauss law in terms of Fock operators. The gauge fields are described in two different bases, based on either group elements or group representations. This formulation allows for a natural scheme to achieve a consistent truncation of the Hilbert space for continuous groups, and provides helpful tools to study the connections of gauge theories with topological quantum double and string-net models for discrete groups. Several examples, including the case of the discrete $D_3$ gauge group, are presented.