Robustness of topology of wavefunctions in NISQ quantum machines

Evaluating topological invariants is an important way to characterize different topological quantum phases, which form a critical component in investigating quantum materials. Topological invariants are quantities that characterize the global geometrical properties of wave functions and thus are immune to local noise. Here we demonstrate a general way to measure the topological invariants on NISQ quantum computers. Due to their robustness, the topological invariants can be precisely obtained even in the presence of local noise, and in certain cases is even noise-free. We apply this approach on IBM quantum computers to a topological superconducting model, and show that strikingly the Chern number can be measured exactly without any error. Other topological invariants are not as robust as the Chern number measurement but can still qualitatively distinguish different topological phases.