Digitizing SU(2) Gauge Fields and What to Look Out for When Doing So

TL;DR

This paper explores various digitization methods for SU(2) gauge fields, analyzing their efficiency and transitions, with a focus on finite subgroups and innovative discretization approaches suitable for quantum and tensor network simulations.

Contribution

It introduces new discretization strategies for SU(2) gauge fields, including a generalized Fibonacci spiral, and examines their effectiveness and phase transitions in the context of quantum computing.

Findings

Fibonacci spiral discretization is highly efficient and near optimal.

Identified a freezing transition at weak couplings.

Compared multiple finite subgroup discretizations for SU(2).

Abstract

With the long term perspective of using quantum computers and tensor networks for lattice gauge theory simulations, an efficient method of digitizing gauge group elements is needed. We thus present our results for a handful of discretization approaches for the non-trivial example of SU(2), such as its finite subgroups, as well as different classes of finite subsets. We focus our attention on a freezing transition observed towards weak couplings. A generalized version of the Fibonacci spiral appears to be particularly efficient and close to optimal.