AGP-based unitary coupled cluster theory for quantum computers

TL;DR

This paper introduces a novel AGP-based unitary coupled cluster method for quantum computers, improving the efficiency of simulating strongly correlated electronic systems by leveraging symmetry restoration and post-selection techniques.

Contribution

The authors develop an AGP-based unitary coupled cluster approach that efficiently restores particle number symmetry and demonstrates its application to the Fermi-Hubbard model.

Findings

Method scales as O(√M) in measurements, reducing cost.

Successfully applied to 1D and 2D Fermi-Hubbard models.

Post-selection effectively restores symmetry with lower measurement overhead.

Abstract

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 a unitary coupled cluster method 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 $\mathcal{O}(\sqrt{M})$ in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry.