  Simulating molecules using the Variational Quantum Eigensolver method is one
of the promising applications for NISQ-era quantum computers. Designing an
efficient ansatz to represent the electronic wave function is crucial in such
simulations. Standard unitary coupled-cluster with singles and doubles (UCCSD)
ansatz tends to have a large number of insignificant terms that do not lower
the energy of the system. In this work, we present a unitary selective
coupled-cluster method, a way to construct a unitary coupled-cluster ansatz
iteratively using a selection procedure with excitations up to fourth order.
This approach uses the electronic Hamiltonian matrix elements and the
amplitudes for excitations already present in the ansatz to find the important
excitations of higher order and to add them to the ansatz. The important
feature of the method is that it systematically reduces the energy error with
increasing ansatz size for a set of test molecules. The main advantage of the
proposed method is that the effort to increase the ansatz does not require any
additional measurements on a quantum computer.
