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

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.

Comments: Proceedings of the 39th International Symposium on Lattice Field Theory, 8th-13th August 2022, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany