AGP-based unitary coupled cluster theory for quantum computers

Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. The same goes for ansatze on a quantum computer. We develop a unitary coupled cluster method based on the antisymmetrized geminal power (AGP)-a state formally equivalent to the number-projected Bardeen-Cooper-Schrieffer wavefunction. We demonstrate our method for the single-band Fermi-Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than O(root M) in the number of measurements, thereby making a less expensive alternative to gauge integration to restore particle number symmetry.