Gluon Digitization via Character Expansion for Quantum Computers

TL;DR

This paper introduces a systematic method for digitizing gauge theories on quantum computers using character expansions, balancing qubit efficiency and systematic errors, with simulations on discrete subgroups of SU(3).

Contribution

It derives a single plaquette action through group character expansions and demonstrates its application with simulations on discrete subgroups of SU(3).

Findings

Derived a systematic digitization scheme for gauge theories.

Performed simulations on discrete SU(3) subgroups up to fifth-order.

Showed the trade-off between qubit efficiency and systematic errors.

Abstract

Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use a smaller, fixed number of qubits at the cost of systematic errors. We systematize this approach by deriving the single plaquette action through matching the continuous group action to that of a discrete one via group character expansions modulo the field fluctuation contributions. We accompany this scheme by simulations of pure gauge over the largest discrete crystal-like subgroup of $SU(3)$ up to the fifth-order in the coupling constant.