Title: Optimal Computation from Fluctuation Responses Show Chinese title

Title: 从涨落响应中进行最优计算

Abstract: The energy cost of computation has emerged as a central challenge at the intersection of physics and computer science. Recent advances in statistical physics -- particularly in stochastic thermodynamics -- enable precise characterizations of work, heat, and entropy production in information-processing systems driven far from equilibrium by time-dependent control protocols. A key open question is then how to design protocols that minimize thermodynamic cost while ensur- ing correct outcomes. To this end, we develop a unified framework to identify optimal protocols using fluctuation response relations (FRR) and machine learning. Unlike previous approaches that optimize either distributions or protocols separately, our method unifies both using FRR-derived gradients. Moreover, our method is based primarily on iteratively learning from sampled noisy trajectories, which is generally much easier than solving for the optimal protocol directly from a set of governing equations. We apply the framework to canonical examples -- bit erasure in a double-well potential and translating harmonic traps -- demonstrating how to construct loss functions that trade-off energy cost against task error. The framework extends trivially to underdamped systems, and we show this by optimizing a bit-flip in an underdamped system. In all computations we test, the framework achieves the theoretically optimal protocol or achieves work costs comparable to relevant finite time bounds. In short, the results provide principled strategies for designing thermodynamically efficient protocols in physical information-processing systems. Applications range from quantum gates robust under noise to energy-efficient control of chemical and synthetic biological networks. Show Chinese abstract

Abstract: 计算的能量成本已成为物理和计算机科学交叉领域的核心挑战。 统计物理的最新进展——特别是随机热力学——使得能够在由时间依赖控制协议驱动的非平衡信息处理系统中精确表征功、热量和熵产生。 一个关键的开放问题是如何设计协议，在确保正确结果的同时最小化热力学成本。 为此，我们开发了一个统一的框架，使用涨落响应关系（FRR）和机器学习来识别最优协议。 与以往分别优化分布或协议的方法不同，我们的方法利用FRR导出的梯度将两者统一起来。 此外，我们的方法主要基于从采样的噪声轨迹中迭代学习，这通常比直接从一组控制方程中求解最优协议要容易得多。 我们将该框架应用于典型示例——双势阱中的位擦除和谐波陷阱的移动——展示了如何构建在能量成本和任务误差之间进行权衡的损失函数。 该框架可以轻松扩展到阻尼不足的系统，并通过优化阻尼不足系统中的位翻转来证明这一点。 在我们测试的所有计算中，该框架实现了理论上最优的协议，或者实现了与相关有限时间界限相当的功耗。 简而言之，这些结果为设计物理信息处理系统中的热力学高效协议提供了有原则的策略。 应用范围包括在噪声下稳健的量子门以及化学和合成生物网络的能量高效控制。