神经网络在量子比特晶格模型中学习符号规则的原则
Principle of learning sign rules by neural networks in qubit lattice models
AI总结：
本研究基于古茨威勒平均场理论，提出用单隐藏神经元浅层前馈神经网络展示量子比特晶格模型中有序态的符号规则，并通过多种模型基准测试验证其可经典可视化及量子涨落对准确率的影响。
摘要：
神经网络是一种强大的工具，能够揭示超越人类直觉的隐藏规律。然而，由于其复杂的非线性结构，它往往表现为一个黑箱。借助古茨威勒平均场理论，我们可以展示量子比特晶格模型中有序态符号规则的一个原则。我们引入一个具有单个隐藏神经元的浅层前馈神经网络来呈现这些符号规则。我们在多种模型中进行了系统的基准测试，包括广义伊辛模型、自旋-$1/2$ XY模型、（阻挫）海森堡环、环面上的三角XY反铁磁体以及任意填充下的费米-哈伯德环。这些基准测试表明，所有主要阶符号规则特征都可以以经典形式可视化，例如俯仰角。此外，量子涨落会导致定量的不完美准确率。
英文摘要：
A neural network is a powerful tool that can uncover hidden laws beyond human intuition. However, it often appears as a black box due to its complicated nonlinear structures. By drawing upon the Gutzwiller mean-field theory, we can showcase a principle of sign rules for ordered states in qubit lattice models. We introduce a shallow feed-forward neural network with a single hidden neuron to present these sign rules. We conduct systematical benchmarks in various models, including the generalized Ising, spin-$1/2$ XY, (frustrated) Heisenberg rings, triangular XY antiferromagnet on a torus, and the Fermi-Hubbard ring at an arbitrary filling. These benchmarks show that all the leading-order sign rule characteristics can be visualized in classical forms, such as pitch angles. Besides, quantum fluctuations can result in an imperfect accuracy rate quantitatively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
