Dynamical signatures of Floquet topological phases in quantum computing

Many body phenomena far from equilibrium present challenges beyond reach by classical computational resources, while digital quantum computers provide a possible way out. Among the intriguing aspects of dynamical many body systems, Floquet phases of matter is an especially rich area for both theoretical and experimental investigations. We propose a scheme to simulate and characterize the many body Floquet systems on a near-term quantum computer. By using a periodic circuit construction, we can then simulate the evolution of a many-body localized Floquet system exhibiting four different phases. We also define a dynamical order parameter for each phases, which can be probed using random measurements. Through numerical simulation we demonstrate that our methods can help distinguish between different Floquet phases. Moreover, our scheme can be properly adjusted to probe new many-body localized Floquet phases with unknown order parameters. Our results can be readily applied to near-term quantum computers such as IBM-Q.