论文标题
从本征征的本地测量中，哈密顿重建的监督学习
Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates
论文作者
论文摘要
通过对其本征态进行测量，重建哈密顿量的系统是量子物理学中的重要反相问题。最近，结果表明，通用多体局部哈密顿量可以通过局部测量回收，而不知道相关函数的值。在这项工作中，我们对不同系统的深度讨论了这个问题，并通过神经网络应用监督的学习方法来解决该方法。对于低洼的本征态，逆问题是良好的，即使使用浅网络和小型数据集，神经网络也是有效且可扩展的。对于中层的本征态，该问题是不适合的，我们提出了一种基于转移学习的修改方法。神经网络还可以根据BFGS方法有效地生成适当的初始点进行数值优化。
Reconstructing a system Hamiltonian through measurements on its eigenstates is an important inverse problem in quantum physics. Recently, it was shown that generic many-body local Hamiltonians can be recovered by local measurements without knowing the values of the correlation functions. In this work, we discuss this problem in more depth for different systems and apply the supervised learning method via neural networks to solve it. For low-lying eigenstates, the inverse problem is well-posed, neural networks turn out to be efficient and scalable even with a shallow network and a small data set. For middle-lying eigenstates, the problem is ill-posed, we present a modified method based on transfer learning accordingly. Neural networks can also efficiently generate appropriate initial points for numerical optimization based on the BFGS method.
