  Quantum computation represents a revolutionary approach for solving problems
in quantum chemistry. However, due to the limited quantum resources in the
current noisy intermediate-scale quantum (NISQ) devices, quantum algorithms for
large chemical systems remains a major task. In this work, we demonstrate that
the circuit depth of the unitary coupled cluster (UCC) and UCC-based ansatzes
in the algorithm of variational quantum eigensolver can be significantly
reduced by an energy-sorting strategy. Specifically, subsets of excitation
operators are first pre-screened from the operator pool according to its
contribution to the total energy. The quantum circuit ansatz is then
iteratively constructed until the convergence of the final energy to a typical
accuracy. For demonstration, this method has been successfully applied to
molecular and periodic systems. Particularly, a reduction of 50\%$\sim$98\% in
the number of operators is observed while retaining the accuracy of the origin
UCCSD operator pools. This method can be straightforwardly extended to general
parametric variational ansatzes.
