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.