Constructing quantum gates for SU(2) and SU(3) gauge theories using discrete groups

Erik Gustafson, Ph.D.; Fermi National Accelerator Laboratory

Discrete groups are a useful approximation to continuous groups for lattice gauge theories in certain coupling regimes. In this talk I will discuss the construction of quantum gates for two discrete groups: the binary tetrahedral group and group S(3x36). These groups are the smallest crystal-like discrete subgroups for SU(2) and SU(3). I will walk through the construction of the group multiplication, trace, inverse, and quantum Fourier transform. I will compare the costs of simulating these theories with other formulations of these gauge theories in the literature. I will also address open problems remaining for optimization.

For those wishing to participate via ZOOM, use Meeting ID 973 3626 5389.