We consider the problem of finding the energy minimum of a complex quantum Hamiltonian by employing a non-Markovian bath prepared in a low energy state. The energy minimization problem is thus turned into a thermodynamic cooling protocol in which we repeatedly put the system of interest in contact with a colder auxiliary system. By tuning the internal parameters of the bath, we show that the optimal cooling is obtained in a regime where the bath exhibits a quantum phase transition in the thermodynamic limit. This result highlights the importance of collective effects in thermodynamic devices. We furthermore introduce a two-step protocol that combines the interaction with the bath with a measure of its energy. While this protocol does not destroy coherence in the system of interest, we show that it can further enhance the cooling effect.
@article{arxiv.2305.06008,
title = {A thermodynamic approach to optimization in complex quantum systems},
author = {Alberto Imparato and Nicholas Chancellor and Gabriele De Chiara},
journal= {arXiv preprint arXiv:2305.06008},
year = {2024}
}