State preparation of AGP on a quantum computer without number projection

TL;DR

This paper presents a deterministic, polynomial-cost quantum algorithm for preparing the antisymmetrized geminal power (AGP) state, equivalent to ESP and PBCS states, without relying on number symmetry restoration.

Contribution

It introduces a novel quantum circuit for AGP state preparation that is deterministic, efficient, and does not depend on number symmetry breaking and restoration techniques.

Findings

The circuit is equivalent to a disentangled unitary paired coupled cluster operator.

It can be implemented with polynomial cost on a quantum computer.

The method captures complex entanglement properties beyond traditional Hartree-Fock methods.

Abstract

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.