A Simple Method for Seniority-Zero Quantum State Preparation

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, starting from an initial state with a sufficiently high overlap with the ground state. For strongly correlated states, where QPE is expected to have an 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 the 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 or if the number of large amplitudes is below 5. We demonstrate that substituting leading oo-pCCD amplitudes into the UpCCD ansatz allows one 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 the approximate preparation of singlet states for QPE and related algorithms.