Quantum simulation of non-Abelian lattice gauge theories

Lattice gauge theories are powerful tools to describe nature and its interactions, finding applications from the theory of Standard Model to condensed matter physics, but there are still many unresolved issues. The recent development of quantum technologies opens the door to new techniques, such as quantum simulation and quantum computation, which can overcome these difficulties and expand our knowledge of these models. There have already been many studies on Abelian lattice gauge theories, but in this thesis we develop an algorithm to investigate non-Abelian lattice gauge theories with dihedral D4 and D3 gauge groups. We describe the gates and the full circuit to prepare the ground state of one and two plaquette systems, given the Hamiltonian and exploiting adiabatic evolution. Then we calculate some relevant observables, such as energy and Wilson loops. All quantum simulations are performed using the open-source Qiskit toolkit. The obtained results are checked against exact diagonalization numerical solutions, with respect to which we find a very good agreement.