Accurately
solving the electronic structure problem through the
variational quantum eigensolver (VQE) is hindered by the available
quantum resources of current and near-term devices. One approach to
relieving the circuit depth requirements for VQE is to “pre-process”
the electronic Hamiltonian by a similarity transformation incorporating
some degree of electronic correlation, with the remaining correlation
left to be addressed by the circuit ansatz. This often comes at the
price of a substantial increase in the number of terms to measure
in the similarity-transformed Hamiltonian. In this work, we propose
an efficient approach to sampling elements from the complete Pauli
group for N qubits which minimizes the onset of new
terms in the transformed Hamiltonian while facilitating substantial
energy lowering. We benchmark the growth-mitigating generator selection
technique for ground state energy estimations applied to models of
the H4, N2, and H2O molecular systems.
It is found that utilizing a selection procedure which obtains the
growth-minimizing generator from the set of operators with the maximal
energy gradient is the most competitive approach to reducing the onset
of Hamiltonian terms while achieving systematic energy lowering of
the reference state.