Efficient Quantum Cooling Algorithm for Fermionic Systems

TL;DR

This paper introduces an efficient quantum cooling algorithm for fermionic systems that prepares ground states using Hamiltonian simulation and a spectroscopic scan, with polynomial runtime under certain spectral gap conditions.

Contribution

The authors develop a novel quantum cooling algorithm for fermionic Hamiltonians that is efficient and generalizes to thermal state preparation, outperforming adiabatic methods in many cases.

Findings

Algorithm has polynomial runtime for systems with polynomially decreasing spectral gaps.

Spectroscopic scan effectively identifies relevant eigenenergies.

Demonstrated on Fermi-Hubbard model with promising results.

Abstract

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 pseudo-adiabatic sweep from a parameter regime whose ground state can be easily prepared. We estimate that our algorithm has a polynomial runtime for systems where the spectral gap decreases at most polynomially in system size, and is faster than the adiabatic algorithm for a large range of settings. We generalize the algorithm to prepare thermal states and demonstrate our findings on the Fermi-Hubbard model.