Simulation of Higher Dimensional Discrete Time Crystals on a Quantum Computer

Abstract: The study of topologically ordered states have given rise to a growing interest in symmetry protected states in quantum matter. Recently, this theory has been extended to quantum many body systems which demonstrate ordered states at low temperature. An example of this is the discrete time crystal (DTC) which has been demonstrated in a real quantum computer and in driven systems. These states are periodic in time and are protected to disorder to a certain extent. In general, DTC can be classified into two phases, the stable many body localization (MBL) state, and the disordered thermal state. This work demonstrates by generalizing DTC to 2 dimensions, there is an decrease in thermal noise and an increase in the operating range of the MBL range in the presence of disorder.