aiqbench analysis
This research introduces a novel quantum kernel framework that integrates anyonic exchange statistics to improve feature-space geometry in machine learning tasks. By unifying bosonic, fermionic, and fractional phases within a single paradigm, the study demonstrates measurable performance gains over traditional symmetric or antisymmetric limits on standard benchmarks. The work establishes particle exchange statistics as a critical computational resource previously underutilized for enhancing quantum model capabilities.
Enhancing Quantum Machine Learning with Anyons
arXiv:2606.16090v1 Announce Type: cross 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.
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.
Quantum Physics (quant-ph); Machine Learning (cs.LG)
arXiv:2606.16090 [quant-ph]
(or arXiv:2606.16090v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.16090 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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