A simple method for seniority-zero quantum state preparation

Abstract: Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of electronic systems using a quantum computer. It requires, however, to be warm--started from an initial state with sufficiently high overlap with the ground state. For strongly-correlated states, where QPE is expected to have advantage over classical methods, preparation of such initial states requires deep quantum circuits and/or expensive hybrid quantum-classical optimization. It is well-known that orbital-optimized paired Coupled Cluster Doubles (oo-pCCD) method can describe the static correlation features of many strongly correlated singlet states. We show that pCCD and its unitary counterpart, UpCCD, become equivalent in the limit of small amplitudes if the amplitude matrix is sufficiently sparse. We demonstrate that substituting leading oo-pCCD amplitudes into the UpCCD Ansatz allows to prepare high-fidelity singlet states for models of multiple-bond dissociation in ethene, ethyne and dinitrogen, as well as for 1D Hubbard models at half-filling, with very shallow circuits. We envisage our method to be of general use for approximate preparation of singlet states for Quantum Phase Estimation and related algorithms.