  Shallow, CNOT-efficient quantum circuits are crucial for performing accurate
computational chemistry simulations on current noisy quantum hardware. Here, we
explore the usefulness of non-iterative energy corrections, based on the method
of moments of coupled-cluster theory, for accelerating convergence toward full
configuration interaction. Our preliminary numerical results relying on
iteratively constructed ans\"{a}tze suggest that chemically accurate energies
can be obtained with substantially more compact circuits, implying enhanced
resilience to gate and decoherence noise.
