Anomalous Floquet topological modes on quantum simulators

We study the dynamics of a collection of engineered Floquet topological phases using superconducting digital quantum simulators. We design a one dimensional topological Floquet insulator which experimentally demonstrates chiral flow—nontrivial particle transport protected by chiral symmetry—with constant-depth quantum circuit optimization. We find that the driving strength acts as a tuning knob to control the resolution of topological modes imaged in the frequency spectrum. We apply our method to realize the dynamics of a one dimensional helical Floquet model exhibiting spin-momentum locking with unidirectional particle motion, and compare with closed system dynamics calculations. Finally, we present the simulated dynamics of an Ising Floquet symmetry-protected topological chain with time-translation symmetry breaking on the boundary.