Ground-State Preparation of the Fermi-Hubbard Model on a Quantum Computer with 2D Topology via Quantum Eigenvalue Transformation of Unitary Matrices

TL;DR

This paper demonstrates a novel quantum algorithm application for preparing the ground state of the 2D Fermi-Hubbard model on a 9-qubit hardware architecture, emphasizing circuit optimization and noise robustness.

Contribution

It introduces a tailored QETU-based method for the 2D Fermi-Hubbard model, including circuit simplifications and hardware mapping strategies for improved feasibility.

Findings

Successful application of QETU to a 2x2 Fermi-Hubbard model

Circuit simplifications for the specific model

Analysis of noise robustness and practical implementation considerations

Abstract

Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of quantum systems. The Fermi-Hubbard model, particularly, is of profound interest due to its implications for high-temperature superconductivity and strongly correlated electron systems. The quantum eigenvalue transformation of unitary matrices (QETU) algorithm offers a novel approach for ground state estimation by utilizing a controlled Hamiltonian time evolution operator, circumventing the resource-intensive block-encoding required by previous methods. In this work, we apply the QETU algorithm to the $2 \times 2$ Fermi-Hubbard model, presenting circuit simplifications tailored to the model and introducing a mapping to a 9-qubit grid-like hardware architecture inspired by fermionic swap networks. We investigate how the selection of a favorable hardware architecture can benefit the circuit construction. Additionally, we explore the feasibility of this method under the influence of noise, focusing on its robustness and practical applicability.