Efficient guiding states for the cascaded variational quantum eigensolver

The Cascaded Variational Quantum Eigensolver (CVQE) algorithm is a quantum variational algorithm for finding the ground state of a Hamiltonian. The CVQE algorithm implements the variational optimization entirely on a classical computer. This classical variational optimization is informed by the measured probability distribution of a guiding state that is obtained from a quantum computer. We explore the efficiency of various quantum circuits for generating useful guiding states. We argue that generating a useful guiding state requires information about the Hamiltonian. By decomposing the Hamiltonian into a sum of Pauli strings, we are able to remove those Pauli strings that do not significantly contribute to the generation of the guiding state. Using the methane molecule as a test system, we determine which Pauli strings in the Hamiltonian decomposition are significant.