Practical implementations of quantum technologies require preparation of states with a high degree of purity—or, in thermodynamic terms, very low temperatures. Given finite resources, the Third Law of thermodynamics prohibits perfect cooling; nonetheless, attainable upper bounds for the asymptotic ground state population of a system repeatedly interacting with quantum thermal machines have recently been derived. These bounds apply within a memoryless (Markovian) setting, in which each refrigeration step proceeds independently of those previous. Here, we expand this framework to study the effects of memory on quantum cooling. By introducing a memory mechanism through a generalized collision model that permits a Markovian embedding, we derive achievable bounds that provide an exponential advantage over the memoryless case. For qubits, our bound coincides with that of heat-bath algorithmic cooling, which our framework generalizes to arbitrary dimensions. We lastly describe the adaptive step-wise optimal protocol that outperforms all standard procedures.

中文翻译：

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通过有限内存效应实现量子冷却的指数改进

量子技术的实际实现要求准备具有高纯度（或者就热力学而言是非常低的温度）的状态。给定有限的资源，热力学第三定律禁止进行完美冷却。然而，最近已经得出了与量子热机反复相互作用的系统的渐近基态种群的可达到上限。这些界限适用于无记忆（马尔可夫式）设置，其中每个制冷步骤均独立于先前的那些步骤进行。在这里，我们扩展这个框架来研究内存对量子冷却的影响。通过允许通用马尔可夫嵌入的通用碰撞模型引入存储机制，我们得出了可实现的边界，与无记忆的情况相比，该边界提供了指数优势。对于量子比特 我们的界限与热浴算法冷却的界限相吻合，我们的框架将其概括为任意尺寸。我们最后描述了优于所有标准程序的自适应逐步最佳协议。