Quantum Simulation of Dihedral Gauge Theories*

In this talk, I describe the simulation of dihedral gauge theories on digital quantum computers. The nonabelian discrete gauge group DN – the dihedral group – serves as an approximation to U(1) × Z2 lattice gauge theory. In order to carry out such a lattice simulation, we detail the construction of efficient quantum circuits to realize basic primitives including the nonabelian Fourier transform over DN, the trace operation, and the group multiplication and inversion operations. For each case the required quantum resources scale linearly or as low-degree polynomials in n = log N. We experimentally benchmark our gates on the Rigetti Aspen-9 quantum processor for the case of D4. The fidelity of all D4 gates was found to exceed 80%.