Enhancing Quantum Machine Learning with Anyons
2026-06-15 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study how different types of quantum particles—bosons, fermions, and anyons—affect quantum machine learning. They introduce a framework that treats all three particle exchange behaviors in one model and show that particles with fractional statistics (anyons) provide access to new data features and improve learning performance. Their analysis shows that anyonic models better separate data and simplify learning compared to bosonic or fermionic ones. This work highlights that particle exchange properties play an important role in shaping quantum machine learning capabilities.
quantum computingquantum machine learningbosonsfermionsanyonsparticle exchange statisticsquantum kernelfeature spaceGram matrixHaar measure
Authors
Da Zhang, Wen-Qiang Liu, Zhaohui Wei, Zhang-Qi Yin
Abstract
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.