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 Ans\"atze on a quantum computer. We develop unitary coupled cluster method antisymmetrized geminal power (AGP) -- state formally equivalent to number-projected Bardeen--Cooper--Schrieffer wavefunction. demonstrate our single-band Fermi--Hubbard Hamiltonian one two dimensions. also explore post-selection as preparation step obtain correlated AGP prove that it scales no worse than $\mathcal{O}(\sqrt{M})$ number of measurements, thereby making less expensive alternative gauge integration restore particle symmetry.