学习未知量子态可降低擦除能耗，实现高效热力学操作。
Learning to erase quantum states: thermodynamic implications of quantum learning theory
- 通过学习获取状态信息，使擦除过程可逆且无能量损耗。
- 擦除能耗与量子态复杂度、纠缠和魔性直接相关。
- 适用于高效学习算法的热力学任务，如能量提取。
擦除量子态的能量成本取决于我们对这些态的了解程度。我们证明，学习算法能够获取此类知识，从而以最优能量成本擦除多个未知态。这通过证明学习过程可完全可逆且本身无基本能量成本来实现。通过简单的计数论证，我们将擦除量子态的能量成本与它们的复杂度、纠缠和魔性联系起来。我们进一步表明，当学习高效时，构造的擦除协议也计算高效。反之，在标准密码学假设下，一般情况下无法高效实现最优能量成本。这些结果还支持基于学习的高效功提取。综上，我们的研究建立了量子学习理论与热力学之间的具体联系，凸显了学习过程的物理意义，并实现了可证明高效的基于学习的热力学协议。
原文摘要 · Abstract (English)
The energy cost of erasing quantum states depends on our knowledge of the states. We show that learning algorithms can acquire such knowledge to erase many copies of an unknown state at the optimal energy cost. This is proved by showing that learning can be made fully reversible and has no fundamental energy cost itself. With simple counting arguments, we relate the energy cost of erasing quantum states to their complexity, entanglement, and magic. We further show that the constructed erasure protocol is computationally efficient when learning is efficient. Conversely, under standard cryptographic assumptions, we prove that the optimal energy cost cannot be achieved efficiently in general. These results also enable efficient work extraction based on learning. Together, our results establish a concrete connection between quantum learning theory and thermodynamics, highlighting the physical significance of learning processes and enabling provably-efficient learning-based protocols for thermodynamic tasks.
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