  Topological quantum phases of quantum materials are defined through their
topological invariants. These topological invariants are quantities that
characterize the global geometrical properties of the quantum wave functions
and thus are immune to local noise. Here, we present a general strategy to
measure topological invariants on NISQ quantum computers and demonstrate our
proposal by applying it to a topological superconducting model. Remarkably, we
find that the Chern numbers of the model can be measured exactly; that is, it
is immune to the noise of NISQ machines. We also evaluate the Zak phase and
ensemble geometric phase, which are not as robust as the Chern number, but
still can be used to qualitatively distinguish different topological phases.
Our study demonstrates that the robust nature of wave function topology allows
noisy NISQ machines to determine topological invariants accurately.
