算子分数匹配用于学习量子哈密顿量

中文摘要 AI 辅助

从低温热态测量中学习量子哈密顿量是量子物理学中的一个基本问题。现有方法的可扩展性受到半定优化问题或配分函数计算复杂性的限制。在此，我们开发了一种经典分数匹配方法的量子类比，利用算子代数中广义导数与分部积分的概念。我们引入了一种新的“算子分数匹配”损失函数，通过简单的梯度下降即可恢复哈密顿量参数，而无需计算难以处理的归一化常数。对横场伊辛模型、XXZ自旋链、费米-哈伯德模型和格点φ^4理论的吉布斯态数值实验表明，使用嵌套交换子展开的有限深度截断即可实现高效的参数恢复。我们的结果确立了算子分数匹配作为一种实用的、无需配分函数的量子哈密顿量学习框架。

英文摘要

Learning quantum Hamiltonians from low-temperature thermal state measurements is a fundamental problem in quantum physics. Scalability of existing methods is limited by the complexity of semidefinite optimization problems or partition function computation. Here, we develop a quantum analog of classical score matching method that exploits generalized notions of derivatives and integration by parts in operator algebras. We introduce a new \emph{Operator Score Matching} loss function that recovers Hamiltonian parameters by a simple gradient descent without the need to compute intractable normalization constants. Numerical experiments on the Gibbs states of the transverse-field Ising model, XXZ spin chain, Fermi-Hubbard model, and lattice $ϕ^4$ theory demonstrate efficient parameter recovery using finite-depth truncations of nested commutator expansions. Our results establish Operator Score Matching as a practical, partition-function-free framework for quantum Hamiltonian learning.

发表机构

• Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）

机构由 AI 辅助整理，请以论文原文为准。