Gluon Field Digitization via Group Space Decimation for Quantum Computers

TL;DR

This paper develops a systematic approach for digitizing gluon fields in quantum computers by deriving a plaquette action that approximates continuous gauge groups using discrete subgroups, and validates it through simulations.

Contribution

It introduces a unified framework for gauge field digitization via group space decimation, improving understanding of approximation accuracy and potential enhancements.

Findings

Derived a single plaquette action for continuous gauge groups

Performed simulations of pure gauge on discrete subgroups of SU(3)

Analyzed systematic errors and approximation effectiveness

Abstract

Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use fewer qubits at the cost of systematic errors. We systematize this approach by deriving a single plaquette action for approximating general continuous gauge groups through integrating out field fluctuations. This provides insight into the effectiveness of these approximations, and how they could be improved. We accompany the scheme by simulations of pure gauge over the largest discrete subgroup of $SU(3)$ up to the third order.