用于相干量子学习的量子哈密顿量演化

中文摘要 AI 辅助

我们提出了相干量子学习（Coherent Quantum Learning, CQL），这是一种量子学习模型的训练框架，其中模型参数为量子自由度，在编码损失函数的哈密顿量下演化。当前量子机器学习保留经典优化：参数由经典外循环通过测量得到的梯度估计值更新，量子相干性在训练动力学中无作用，与该问题的任何经典处理一致。在量子情形下，初始化于叠加态的参数寄存器幺正演化，概率幅通过干涉集中于低损失构型附近，无需梯度计算或经典反馈。我们给出了使用块编码和哈密顿量模拟的显式构造，适用于任意参数化电路。针对二分类和干涉相位估计的数值实验证实，演化后的分布在最优参数处达到峰值，与基于梯度的性能匹配。该构造原则上与容错实现兼容，可通过顺序哈密顿量演化扩展至批量训练。

英文摘要

We introduce Coherent Quantum Learning (CQL), a training framework for quantum learning models in which the model parameters are quantum degrees of freedom evolved under a Hamiltonian that encodes the loss function. Current quantum machine learning retains classical optimization: parameters are updated by a classical outer loop using gradient estimates from measurements, and quantum coherence has no role in the training dynamics, just as in any classical treatment of the same problem. In the quantum case, a parameter register initialized in superposition evolves unitarily, and probability amplitude concentrates near low-loss configurations through interference, without gradient computation or classical feedback. We give an explicit construction using block encodings and Hamiltonian simulation, applicable to arbitrary parameterized circuits. Numerical experiments on binary classification and interferometric phase estimation confirm that the evolved distribution peaks at the optimal parameters, matching gradient-based performance. The construction is compatible in principle with fault-tolerant implementations and extends to batched training via sequential Hamiltonian evolution.

发表机构

• Quantum Mads（量子麦兹）
• Department of Physical Chemistry, University of the Basque Country UPV/EHU（巴斯克大学物理化学系）
• EHU Quantum Center, University of the Basque Country UPV/EHU（巴斯克大学EHU量子中心）
• TECNALIA, Basque Research and Technology Alliance (BRTA)（特克拉尼亚，巴斯克研究与技术联盟）
• Institute for Quantum Science and Technology, University of Calgary（卡尔加里大学量子科学与技术研究所）
• Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）

机构由 AI 辅助整理，请以论文原文为准。