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.

中文翻译：

---

复杂量子系统优化的热力学方法

我们考虑通过采用低能态制备的非马尔可夫浴来找到复杂量子哈密顿量的能量最小值的问题。因此，能量最小化问题转化为热力学冷却协议，其中我们反复将感兴趣的系统与更冷辅助系统。通过调整浴的内部参数，我们表明，在浴在热力学极限内表现出量子相变的状态下获得了最佳冷却。这一结果凸显了热力学装置中集体效应的重要性。我们还引入了一个两步协议，将与浴的相互作用与其能量测量结合起来。虽然该协议不会破坏感兴趣系统的一致性，但我们表明它可以进一步增强冷却效果。