  Further advancement of quantum computing (QC) is contingent on enabling
many-body models that avoid deep circuits and excessive use of CNOT gates. To
this end, we develop a QC approach employing finite-order connected moment
expansions (CMX) and affordable procedures for initial state preparation. We
demonstrate the performance of our approach employing several quantum variants
of CMX through the classical emulations on the H2 molecule potential energy
surface and the Anderson model with a broad range of correlation strength. The
results show that our approach is robust and flexible. Good agreements with
exact solutions can be maintained even at the dissociation and strong
correlation limits.
