Correlating AGP on a quantum computer

TL;DR

This paper demonstrates an efficient quantum implementation of the antisymmetrized geminal power (AGP) wavefunction, enabling accurate simulations of strongly correlated systems with low-cost quantum circuits.

Contribution

It introduces a method to implement AGP on quantum computers with linear circuit depth and measurement cost, and benchmarks a unitary correlator on the pairing Hamiltonian.

Findings

Achieves highly accurate ground state energies across correlation regimes

Demonstrates linear scaling in circuit depth and measurements

Validates the effectiveness of AGP-based ansatz for strongly correlated systems

Abstract

For variational algorithms on the near term quantum computing hardware, it is highly desirable to use very accurate ansatze with low implementation cost. Recent studies have shown that the antisymmetrized geminal power (AGP) wavefunction can be an excellent starting point for ansatze describing systems with strong pairing correlations, as those occurring in superconductors. In this work, we show how AGP can be efficiently implemented on a quantum computer with circuit depth, number of CNOTs, and number of measurements being linear in system size. Using AGP as the initial reference, we propose and implement a unitary correlator on AGP and benchmark it on the ground state of the pairing Hamiltonian. The results show highly accurate ground state energies in all correlation regimes of this model Hamiltonian.