Solving the Hubbard model using density matrix embedding theory and the variational quantum eigensolver

TL;DR

This paper explores combining density matrix embedding theory with the variational quantum eigensolver to efficiently compute the ground state of the Hubbard model on quantum computers, demonstrating promising results up to 16 qubits.

Contribution

It introduces a detailed implementation of DMET with VQE for the Hubbard model, including exact embedded Hamiltonian derivation and optimized quantum circuits.

Findings

Effective reproduction of ground state properties for Hubbard model

Successful simulation up to 16 qubits

Enhanced efficiency of quantum algorithms for embedding methods

Abstract

Calculating the ground state properties of a Hamiltonian can be mapped to the problem of finding the ground state of a smaller Hamiltonian through the use of embedding methods. These embedding techniques have the ability to drastically reduce the problem size, and hence the number of qubits required when running on a quantum computer. However, the embedding process can produce a relatively complicated Hamiltonian, leading to a more complex quantum algorithm. In this paper we carry out a detailed study into how density matrix embedding theory (DMET) could be implemented on a quantum computer to solve the Hubbard model. We consider the variational quantum eigensolver (VQE) as the solver for the embedded Hamiltonian within the DMET algorithm. We derive the exact form of the embedded Hamiltonian and use it to construct efficient ansatz circuits and measurement schemes. We conduct detailed numerical simulations up to 16 qubits, the largest to date, for a range of Hubbard model parameters and find that the combination of DMET and VQE is effective for reproducing ground state properties of the model.