A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer

TL;DR

This paper proposes a quantum computing method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model, overcoming classical computational limitations for complex fermionic systems.

Contribution

It introduces a theoretical approach to map the cluster solver of the Fermi-Hubbard model onto a quantum computer, enabling scalable simulations.

Findings

Quantum memory scales with the number of orbitals

Few tens of qubits can simulate complex lattices

Overcomes classical exponential memory limitations

Abstract

Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamical properties can be computed from its grand canonical potential according to standard procedures. In general, there is no closed form solution for lattices of more than one spatial dimension, but solutions can be approximated with cluster perturbation theory. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists in finding its self-energy through a variational principle of the grand canonical potential. This opens the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. Here it is shown theoretically that that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory scales as the number of orbitals in the simulated cluster. A quantum computer with a few tens of qubits could therefore simulate the thermodynamical properties of complex fermionic lattices inaccessible to classical supercomputers.