将物理定律融入进化算法,提升量子控制的精度与鲁棒性。
Physics-Informed Evolution: An Evolutionary Framework for Solving Quantum Control Problems Involving the Schrödinger Equation
- 在适应度函数中嵌入薛定谔方程物理约束,引导进化搜索。
- 在三类量子系统中实现高保真度态制备,状态偏差低于1%
- 适合研究量子控制与进化计算交叉领域的学者参考。
物理信息神经网络(PINNs)表明,将物理定律直接嵌入学习目标可显著提升神经网络解的效率与物理一致性。类似机器学习中优化损失函数,进化算法通过模拟自然选择过程迭代优化目标函数。受此启发,我们提出物理信息进化(PIE)框架,将由基本物理定律导出的信息融入进化适应度景观,从而将物理信息人工智能方法从机器学习拓展至进化计算领域。作为具体应用,我们将PIE用于由薛定谔方程支配的量子控制问题,目标是寻找能将量子系统从初态驱动至目标态的最优控制场。我们在三类代表性量子控制基准上验证PIE:V型三能级系统态制备、超导量子电路纠缠态生成及两原子腔量子电动力学系统。在该框架下,系统比较了十种单目标与五种多目标进化算法。实验结果表明,通过在适应度函数中嵌入物理信息,PIE有效引导进化搜索,获得高保真度、低状态偏差且跨场景鲁棒的控制场。研究进一步表明,物理信息原则可自然延伸至更广泛的进化计算领域。
原文摘要 · Abstract (English)
Physics-informed Neural Networks (PINNs) show that embedding physical laws directly into the learning objective can significantly enhance the efficiency and physical consistency of neural network solutions. Similar to optimizing loss functions in machine learning, evolutionary algorithms iteratively optimize objective functions by simulating natural selection processes. Inspired by this principle, we ask a natural question: can physical information be similarly embedded into the fitness function of evolutionary algorithms? In this work, we propose Physics-informed Evolution (PIE), a novel framework that incorporates physical information derived from governing physical laws into the evolutionary fitness landscape, thereby extending Physics-informed artificial intelligence methods from machine learning to the broader domain of evolutionary computation. As a concrete instantiation, we apply PIE to quantum control problems governed by the Schrödinger equation, where the goal is to find optimal control fields that drive quantum systems from initial states to desired target states. We validate PIE on three representative quantum control benchmarks: state preparation in V-type three-level systems, entangled state generation in superconducting quantum circuits, and two-atom cavity QED systems. Within the PIE framework, we systematically compare the performance of ten single-objective and five multi-objective evolutionary algorithms. Experimental results demonstrate that by embedding physical information into the fitness function, PIE effectively guides evolutionary search, yielding control fields with high fidelity, low state deviation, and robust performance across different scenarios. Our findings further suggest that the Physics-informed principle extends naturally beyond neural network training to the broader domain of evolutionary computation.
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