  The accurate computation of properties of large molecular systems is
classically infeasible and is one of the applications in which it is hoped that
quantum computers will demonstrate an advantage over classical devices.
However, due to the limitations of present-day quantum hardware,
variational-hybrid algorithms introduced to tackle these problems struggle to
meet the accuracy and precision requirements of chemical applications. Here, we
apply the Quantum Computed Moments (QCM) approach combined with a variety of
noise-mitigation techniques to an 8 qubit/spin-orbital representation of the
water molecule (H$_2$O). A noise-stable improvement on the variational result
for a 4-excitation trial-state (circuit depth 25, 22 CNOTs) was obtained, with
the ground-state energy computed to be within $1.4\pm1.2$ mHa of exact
diagonalisation in the 14 spin-orbital basis. Thus, the QCM approach, despite
an increased number of measurements and noisy quantum hardware (CNOT error
rates c.1% corresponding to expected error rates on the trial-state circuit of
order 20%), is able to determine the ground-state energy of a non-trivial
molecular system at the required accuracy (c.0.1%). To the best of our
knowledge, these results are the largest calculations performed on a physical
quantum computer to date in terms of encoding individual spin-orbitals
producing chemically relevant accuracy, and a promising indicator of how such
hybrid approaches might scale to problems of interest in the
low-error/fault-tolerant regimes as quantum computers develop.
