Quantum Simulation using Discrete Gauge Groups

Quantum simulation is the idea of using quantum devices in order to perform numerical simulations in currently inaccessible regimes. Its most natural formulation is in the Hamiltonian picture with a finite-dimensional Hilbert space. For gauge theories, among several possibilities, one can achieve this by replacing the gauge group, a Lie group, with one of its discrete finite subgroups. We start with the Hamiltonian formulation of gauge theories and show what are various possibilities to obtain a finite-dimensional Hilbert  space. We then discuss the case of finite gauge groups, and what are the advantages and disadvantages of this approach. Finally, we outline some of the results on this topic in our recent paper.