标题： 量子机器学习在多量子位相空间 第一卷：基础 显示英文标题

标题： Quantum Machine Learning in Multi-Qubit Phase-Space Part I: Foundations

摘要： 量子机器学习（QML）旨在利用量子力学系统的固有特性，包括叠加、相干性和量子纠缠，用于经典数据处理。 然而，由于希尔伯特空间的指数增长，QML在使用量子系统状态向量表示的经典模拟中面临实际限制。 另一方面，相空间方法通过将量子态编码为准概率函数提供了另一种方法。 基于之前在量子比特相空间和斯特拉托诺维奇-维尔（SW）对应关系上的工作，我们在相空间中构建了一个封闭且可组合的动力学形式化，适用于单个和多个量子比特系统。 该形式化将保罗群的算子代数替换为辛流形上的函数动力学，并将维度灾难重新表述为与量子比特数量线性相关的区域上的谐波支持。 它为基于相空间上的变分建模的QML开辟了一条新途径。 显示英文摘要

摘要： Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of the Hilbert space, QML faces practical limits in classical simulations with the state-vector representation of quantum system. On the other hand, phase-space methods offer an alternative by encoding quantum states as quasi-probability functions. Building on prior work in qubit phase-space and the Stratonovich-Weyl (SW) correspondence, we construct a closed, composable dynamical formalism for one- and many-qubit systems in phase-space. This formalism replaces the operator algebra of the Pauli group with function dynamics on symplectic manifolds, and recasts the curse of dimensionality in terms of harmonic support on a domain that scales linearly with the number of qubits. It opens a new route for QML based on variational modelling over phase-space.