  The determination of ground state properties of quantum systems is a
fundamental problem in physics and chemistry, and is considered a key
application of quantum computers. A common approach is to prepare a trial
ground state on the quantum computer and measure observables such as energy,
but this is often limited by hardware constraints that prevent an accurate
description of the target ground state. The quantum computed moments (QCM)
method has proven to be remarkably useful in estimating the ground state energy
of a system by computing Hamiltonian moments with respect to a suboptimal or
noisy trial state. In this paper, we extend the QCM method to estimate
arbitrary ground state observables of quantum systems. We present preliminary
results of using QCM to determine the ground state magnetisation and spin-spin
correlations of the Heisenberg model in its various forms. Our findings
validate the well-established advantage of QCM over existing methods in
handling suboptimal trial states and noise, extend its applicability to the
estimation of more general ground state properties, and demonstrate its
practical potential for solving a wide range of problems on near-term quantum
hardware.
