  We present a cooling algorithm for ground state preparation of fermionic
Hamiltonians. Our algorithm makes use of the Hamiltonian simulation of the
considered system coupled to an ancillary fridge, which is regularly reset to
its known ground state. We derive suitable interaction Hamiltonians that
originate from ladder operators of the free theory and initiate resonant gaps
between system and fridge. We further propose a spectroscopic scan to find the
relevant eigenenergies of the system using energy measurements on the fridge.
With these insights, we design a ground state cooling algorithm for fermionic
systems that is efficient, i.e. its runtime is polynomial in the system size,
as long as the initial state is prepared in a low energy sector of polynomial
size. We achieve the latter via a fast, quasi-adiabatic sweep from a parameter
regime whose ground state can be easily prepared. We generalize the algorithm
to prepare thermal states and demonstrate our findings on the Fermi-Hubbard
model.
