Signatures of interacting Floquet phases in shallow quantum circuits

Abstract

Many-body phenomena far from equilibrium present challenges beyond reach by classical computational resources. Digital quantum computers provide a possible way forward but noise limits their use in the near term. We propose a scheme to simulate and characterize many-body Floquet systems hosting a rich variety of phases that operates with a shallow circuit, defined as a quantum circuit that does not scale with system sizes. Starting from a periodic circuit that simulates the dynamical evolution of a Floquet system, we introduce quasiperiodicity to the circuit parameters to prevent thermalization by introducing many-body localization. By inspecting the time-averaged properties of the many-body integrals of motion, the phase structure can then be probed using random measurements. This approach avoids the need to compute the ground state and operates at finite energy density. We numerically demonstrate this scheme with a simulation of the Floquet Ising model of time crystals and present results clearly distinguishing different Floquet phases that are protected by many-body localization. Our results pave the way for mapping out phase diagrams of exotic systems on near-term quantum devices.