Dynamics of Symmetry-Protected Topological Phases of Matter on a Quantum Computer

Topological modes are desirable for their capacity to encode quantum information resiliently against external noise. Their implementation on quantum hardware, however, remains a long standing problem due to current limitations of circuit depth and noise, which grow with the number of time-steps. We investigate the time evolution of bulk and surface modes in topological insulator systems realized on coupled noisy intermediate-scale quantum (NISQ) processors, and compare them with closed-system quantum dynamics simulations. By utilizing time-step compression of constant-depth circuits, we demonstrate a method to simulate their long-time dynamics on NISQ hardware and find robust signatures of localized topological modes. We identify a class of one-dimensional topological Hamiltonians with chiral symmetry that can be readily simulated on noisy quantum hardware with circuit depth that is invariant with time. Our results provide a pathway towards stable long-time implementation of interacting many-body systems on present day quantum processors.