Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation

TL;DR

This paper introduces a hybrid quantum-classical method to implement the Gutzwiller wave function using a discrete Hubbard-Stratonovich transformation, enabling quantum simulations of the Hubbard model with experimental validation.

Contribution

It presents a novel hybrid scheme that expresses the Gutzwiller factor as a sum of unitary operators, facilitating quantum simulation of strongly correlated systems.

Findings

Successfully simulated the two-site Fermi-Hubbard model on a quantum device.

Reproduced the exact ground-state energy within error bars.

Demonstrated the scheme's effectiveness with numerical and experimental results.

Abstract

We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using a discrete Hubbard-Stratonovich transformation, which allows us to express the Gutzwiller factor as a linear combination of unitary operators involving only single-qubit rotations, at the cost of the sum over the auxiliary fields. To perform the sum over the auxiliary fields, we introduce two approaches that have complementary features. The first approach employs a linear-combination-of-unitaries circuit, which enables one to probabilistically prepare the Gutzwiller wave function on a quantum computer, while the second approach uses importance sampling to estimate observables stochastically, similar to a quantum Monte Carlo method in classical computation. The proposed scheme is demonstrated with numerical simulations for the half-filled Fermi-Hubbard model. Furthermore, we perform quantum simulations using a real quantum device, demonstrating that the proposed scheme can reproduce the exact ground-state energy of the two-site Fermi-Hubbard model within error bars.