arXiv:2607.05000quant-phcond-mat.stat-mech2026-07被引 1

将神经元进行量子化,构建可处理量子数据的新型神经网络模型。

Canonical quantization of neurons

  • 基于经典能量函数与激活函数的组合,用量子哈密顿量替代能量项。
  • 在量子数据上实现函数逼近,表现优于经典神经元。
  • 适合研究量子机器学习、量子数据处理的学者参考。

经典量子化提供从经典哈密顿量构造量子模型的系统方法。本文将该方法应用于机器学习的基本计算单元——神经元:将神经元视为能量函数与激活函数的组合,通过用量子哈密顿量替换能量函数,并借助矩阵函数微积分施加激活函数,得到可在输入量子态上测量的激活可观测量。我们研究了这些量子化神经元在函数逼近中的应用,目标是从带标签的量子数据中学习未知可观测量。为此,开发了混合量子-经典训练与评估算法,包括激活可观测量的测量方法及平方损失梯度估计方法。梯度估计依赖于经典随机采样、Hadamard测试和哈密顿量模拟等基础技术;可观测量测量则利用单模量子比特幂(power of one qumode)和薛定谔化(Schroedingerization)等量子算法。数值实验表明,量子化神经元在典型学习任务中相比对应经典神经元具有更强的表达能力。本工作确立了经典量子化作为构建量子机器学习基础单元的原理性框架,并为面向量子数据的神经架构设计奠定了基础。

原文摘要 · Abstract (English)

Canonical quantization provides a systematic procedure for constructing quantum models from classical Hamiltonians. Here, we apply this principle to a fundamental computational primitive of machine learning: the neuron. Specifically, by viewing a neuron as a composition of an energy function and an activation function, we quantize this model by replacing the energy function with a quantum Hamiltonian and applying the activation function to it through matrix functional calculus. This results in an activation observable that can be measured on an input quantum state. We investigate the use of these quantized neurons for function approximation, where the objective is to learn an unknown observable from labeled quantum data. For this purpose, we develop hybrid quantum-classical algorithms for training and evaluation, including procedures for measuring the activation observable and estimating gradients of the squared loss error. Our algorithms for gradient estimation rely on basic primitives like classical random sampling, the Hadamard test, and Hamiltonian simulation, and those for measuring an activation observable rely on quantum algorithms known as the power of one qumode and Schroedingerization. Numerical experiments demonstrate that our quantized neurons exhibit enhanced expressive capabilities relative to corresponding classical neurons on representative learning tasks. Our work establishes canonical quantization as a principled framework for constructing quantum machine learning primitives and provides a foundation for developing neural architectures tailored to quantum data.

量子神经网络量子机器学习可观测量

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