When Does Interference Help Learning? Kernel Geometry as a Pre-Experimental Test for Photonic Reservoir Computing

Title:When Does Interference Help Learning? Kernel Geometry as a Pre-Experimental Test for Photonic Reservoir Computing

Abstract:Multi-photon interference is the resource most native to photonic quantum machine learning, yet experiments on photonic reservoirs have reported advantages, null results, and train-only effects. These outcomes cannot be compared: each measures task-dependent accuracy on different tasks and platforms. Here we resolve the question task-independently through the kernel geometry of boson-sampling feature maps. Interference redistributes feature variance across roughly twice as many effective dimensions as distinguishable-particle statistics, generating a large geometric separation between the corresponding kernels. The separation grows superlinearly with indistinguishability, is linear in Hong--Ou--Mandel visibility at small visibility for two to four photons, and retains approximately 80% of its magnitude at the source quality of current quantum processors. Under experimental sampling budgets the separation is learnable on adversarially constructed tasks (accuracy advantage +0.22 plus or minus 0.05) and an order of magnitude smaller on natural tasks, gated by kernel--task alignment. The results reconcile the existing experimental record and supply a pre-experimental protocol: kernel geometry establishes that an interference-specific learning resource exists, and task alignment determines whether a given task can access it; both are computable before committing significant hardware resources.

Quantum Physics (quant-ph); Computational Engineering, Finance, and Science (cs.CE)

arXiv:2610.11360 [quant-ph]

(or arXiv:2610.11360v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.11360 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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