  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.
