Probing entanglement dynamics and topological transitions on noisy
  intermediate-scale quantum computers
We simulate quench dynamics of the Su-Schrieffer-Heeger (SSH) chain on the
IBM quantum computers, calculating the R\'enyi entanglement entropy, the twist
order parameter and the Berry phase. The latter two quantities can be deduced
from a slow-twist operator defined in the Lieb-Schultz-Mattis theorem. The
R\'enyi entropy is obtained using a recently developed randomized measurement
scheme. The twist order parameter and the Berry phase are measured without the
need for additional gates or ancilla qubits. We consider quench protocols in
which a trivial initial state evolves dynamically in time under the topological
SSH Hamiltonian in the fully dimerized limit (the flat-band limit). During
these quenches, there are persistent and periodic oscillations in the time
evolution of both entanglement entropy and twist order parameter. Through the
implementation of error mitigation techniques using a global depolarizing
ansatz and postselection, our simulations on the IBM devices yield results that
closely match exact solutions.
Huai-Chun Chang Hsiu-Chuan Hsu Yu-Cheng Lin