We study the performance of our previously proposed projective
quantum eigensolver (PQE) on IBM’s quantum hardware in conjunction
with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree
(2.5 kcal/mol) of the exact energy along the entire potential energy
curve, with the accuracy limited by both the stochastic error and
the inconsistent performance of the IBM devices. We find that an optimization
algorithm using direct inversion of the iterative subspace can converge
swiftly, even to excited states, but stochastic noise can prompt large
parameter updates. For the 4-site transverse-field Ising model at
its critical point, PQE with an appropriate application of qubit tapering
can recover 99% of the correlation energy, even after discarding several
parameters. The large number of CNOT gates needed for the additional
parameters introduces a concomitant error that, on the IBM devices,
results in a loss of accuracy despite the increased expressivity of
the trial state. Error extrapolation techniques and tapering or postselection
are recommended to mitigate errors in PQE hardware experiments.