Quantum simulation of Thouless pump on quantum hardware*

We demonstrate the simulation of Thouless pump in a XY spin chain in the presence of staggered field on IonQ quantum hardware. The important ingredient of the Thouless pump is that the system should be evolving adiabatically. Therefore, the conventional quantum simulations based on Trotter decomposition would result in a circuit with large depth, which complicates achieving good results even for a short chain formed from several qubits. Here we map the original spin model to a free fermion model, which is identical to the Rice-Mele model, so that we can utilize a powerful compiling method to construct fixed depth circuits and simulate the Thouless pump with arbitrary small Trotter step. We show that with this technique, the clear features of Thouless pump can be identified on quantum hardware.