具有量子态可见单元的受限玻尔兹曼机

中文摘要 AI 辅助

我们构建了一个受限玻尔兹曼机（RBM），其可见输入是量子态而非经典构型。每个隐藏单元携带一个由参数化电路制备的可训练量子模板，并将其与输入的重叠转换为特征。将量子态视为高维连续可见对象会引发非平凡的归一化和缩放问题。我们对连续似然进行正则化，并推导出两个受控的高维极限，分别产生具有连续希尔伯特空间模式的Hopfield型网络和一种数据增强的Gram似然。所得算法紧凑，并使用可训练的电路制备模板作为量子数据与经典优化之间的测量中介。在多个多体系统上的数值模拟展示了有效的量子相识别和多组分特征提取。

英文摘要

We construct a restricted Boltzmann machine (RBM) whose visible input is a quantum state rather than a classical configuration. Each hidden unit carries a trainable quantum template prepared by a parametrized circuit and converts its overlap with the input into a feature. Treating quantum states as high-dimensional continuous visible objects creates nontrivial normalization and scaling problems. We regularize the continuous likelihood and derive two controlled high-dimensional limits, yielding a Hopfield-type network with continuous Hilbert-space patterns and a data-augmented Gram likelihood. The resulting algorithms are compact and use trainable circuit-prepared templates as measurement intermediaries between quantum data and classical optimization. Numerical simulations across several many-body systems demonstrate effective quantum-phase recognition and multicomponent feature extraction.

发表机构

• Institute for Advanced Study in Physics and School of Physics, Zhejiang University（浙江大学物理学院和高等研究院）
• Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院武汉物理与数学研究所）

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