  The iterative quantum phase estimation algorithm, applied to calculating the
ground state energies of quantum chemical systems, is theoretically appealing
in its wide scope of being able to handle both weakly and strongly correlated
regimes. However, the goodness of the initial state that is sent as an input to
the algorithm could strongly decide the quality of the results obtained. In
this work, we generate the initial state by using the classical-quantum hybrid
variational quantum eigensolver algorithm with unitary coupled cluster ansatz.
We apply the procedure to obtain the ground state energies of the H4 molecule
on a circle, as the system exhibits an interplay of dynamic as well as static
correlation effects at different geometries. Furthermore, we argue on the
importance of static correlation in construction of the reference determinant,
and propose a minimally parametrized unitary coupled cluster ansatz, which
drastically reduces number of variational parameters while incorporating the
static correlation effects in the wavefunction. We demonstrate that a carefully
and appropriately prepared initial state can greatly reduce the effects of
noise due to sampling in the estimation of the desired eigenphase.

Quantum Physics