Unitary Selective Coupled Cluster Method

Variational quantum eigensolver is one of the promising methods to simulate quantum systems by utilizing near-term quantum computers. Unitary coupled cluster (UCC) is one of the most promising ways of representing electronic wave function on a quantum computer. Although UCC is a chemistry-inspired ansatz, which only explores chemically relevant parts of the Hilbert space, it often contains too many fermionic operators with nearly zero contribution to the correlation energy of a molecule. We demonstrate that molecular symmetries can be leveraged to pre-screen the excitation operators in the ansatz. Our approach allows us to significantly reduce the number of excitation operators in ansatz. For highly symmetric molecules, this reduction can be up to 80-90%. Moreover, we propose a unitary selective coupled cluster, an iterative method, which can construct a unitary coupled cluster (UCC) ansatz with excitation operators of arbitrary order. We demonstrate its performance on a set of small molecules and discuss the method's potential for simulations of chemical systems on quantum computers.