  Programmable quantum processors are suitable platforms for simulating quantum
systems, of which topological phases are of particular interest. We simulate
the quench dynamics of a one-dimensional system on IBM Q devices. The
topological properties of the dynamics are described by the dynamical
topological invariants, the dynamical winding number and the time-dependent
Berry phase, which are simulated with the quantum circuit model. The results
show that despite the noise present in the current quantum computers, the
dynamical topological invariants are robust. Moreover, to investigate the
influence of open quantum system, we analytically solve the master equation in
Lindblad form and show that the dynamical winding number and the change in
Berry phase are not affected by the dissipation. This study sheds light on the
robustness of topological phases on the noisy intermediate-scale quantum
computers.
