The power of quantum computing and quantum machine learning relies on harnessing uniquely quantum phenomena as computational resources. While superposition, coherence and entanglement have been central to this effort, the role of particle exchange statistics remains largely unexplored. Here, we introduce a quantum kernel framework that unifies bosonic, fermionic, and anyonic (fractional) exchange statistics within a single learning paradigm. We study this family of kernels from three perspectives. At the representation level, Haar-averaged effective-dimension analysis shows that fractional exchange phases access feature-space directions inaccessible to the purely symmetric or antisymmetric limits. At the level of kernel geometry, the corresponding Gram matrices show greater separation from the distinguishable-particle baseline and reduced label-dependent model complexity. Finally, on learning benchmarks, anyonic kernels consistently outperform their bosonic and fermionic counterparts, with stronger target alignment and more favorable class geometry. Together, these findings show that exchange statistics reshape the structure and geometry of quantum feature space, leading to enhanced learning performance. Our work identifies particle exchange statistics as an overlooked computational ingredient for quantum machine learning and provides the first systematic comparison of quantum learning models across exchange phases.

翻译：量子计算与量子机器的学习能力依赖于将独特的量子现象作为计算资源加以利用。虽然叠加、相干和纠缠一直是这一努力的核心，但粒子交换统计的作用在很大程度上仍未得到探索。在此，我们引入一个量子核框架，将玻色子、费米子和任意子（分数）交换统计统一在单一学习范式内。我们从三个角度研究这一族核函数。在表征层面，Haar平均有效维度分析表明，分数交换相位能够访问纯粹对称或反对称极限无法访问的特征空间方向。在核几何层面，对应的Gram矩阵与可区分粒子基线相比表现出更大的分离度，并降低了标签依赖的模型复杂度。最后，在学习基准测试中，任意子核始终优于其玻色子和费米子对应物，具有更强的目标对齐性和更有利的类别几何结构。总之，这些发现表明交换统计重塑了量子特征空间的结构与几何，从而带来学习性能的提升。我们的工作将粒子交换统计确定为量子机器学习中一个被忽视的计算要素，并首次系统比较了跨交换相位的量子学习模型。