  The antisymmetrized geminal power (AGP) is equivalent to the number projected
Bardeen-Cooper-Schrieffer (PBCS) wavefunction. It is also an elementary
symmetric polynomial (ESP) state. We generalize previous research on
deterministically implementing the Dicke state to a state preparation algorithm
for an ESP state, or equivalently AGP, on a quantum computer. Our method is
deterministic and has polynomial cost, and it does not rely on number symmetry
breaking and restoration. We also show that our circuit is equivalent to a
disentangled unitary paired coupled cluster operator and a layer of unitary
Jastrow operator acting on a single Slater determinant. The method presented
herein highlights the ability of disentangled unitary coupled cluster to
capture non-trivial entanglement properties that are hardly accessible with
traditional Hartree-Fock based electronic structure methods.
