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arXiv:2610.11360

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

Oishik Kar, Aswath Babu H

On Aqora:OISHIK KAR IIIT DharwadOISHIK KAR IIIT Dharwad
quant-phcs.CESubmitted Oct 8, 2026• Announced Oct 9, 2026• 0 citations
v1 · Oct 8, 2026v2 · Oct 9, 2026v3 · Oct 12, 2026
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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.

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15 pages 5 figures

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Quantum kernel methods are the most concrete near-term proposal for quantum machine learning on classical data, yet published benchmarks disagree on whether they outperform tuned classical kernels, and the disagreement cannot be resolved from the literature because the comparisons are not protocol-controlled. We argue that the obstacle is one of measurement, not theory: the usual setup fixes the quantum feature map's data scaling while grid-searching the classical kernel's hyperparameters, recomputes nothing per fold, and reports cost in simulator time. We therefore treat the comparison itself as the object of study and impose three controls. The bandwidth is tuned on the same grid budget as the classical γγγ, the kernel is recomputed inside every fold from fold-fitted preprocessing, and cost is counted in hardware circuit evaluations. On top of these we run a factorial design of 324 cells in which dimensionality, training size, class separability and data structure are explicit covariates, together with four standard datasets, a shots-versus-gate-noise ablation, and a cost sweep. The dominant effect we measure is not quantum: tuning the feature map's bandwidth is worth 0.120 accuracy on synthetic data and 0.339 on real data, exceeding every quantum-classical difference we observe. Tuned quantum kernels are then statistically indistinguishable from a tuned RBF on all four real datasets. The advantage on synthetic data is confined almost entirely to data generated by the feature map itself, and it shrinks with dimensionality (-0.0045 per qubit) while growing with sample size. Finite sampling costs an order of magnitude more accuracy than gate and readout noise, and a fidelity kernel needs 5×1075\times10^{7}5×107 circuits at n = 10,000. Protocol variance is thus sufficient to explain the field's contradictory conclusions.
Several photonic quantum technologies rely on the ability to generate multiple indistinguishable photons. Benchmarking the level of indistinguishability of these photons is essential for scalability. The Hong-Ou-Mandel dip provides a benchmark for the indistinguishability between two photons, and extending this test to the multi-photon setting has so far resulted in a protocol that computes the genuine n-photon indistinguishability (GI). However, this protocol has a sample complexity that increases exponentially with the number of input photons for an estimation of GI up to a given additive error. To address this problem, we introduce new theorems that strengthen our understanding of the relationship between distinguishability and the suppression laws of the quantum Fourier transform interferometer (QFT). Building on this, we propose a protocol using the QFT for benchmarking GI that achieves constant sample complexity for the estimation of GI up to a given additive error for prime photon numbers, and sub-polynomial scaling otherwise, representing an exponential improvement over the state of the art. We prove the optimality of our protocol in many relevant scenarios and validate our approach experimentally on Quandela's reconfigurable photonic quantum processor, where we observe a clear advantage in runtime and precision over the state of the art. We therefore establish the first scalable method for computing multi-photon indistinguishability, which applies naturally to current and near-term photonic quantum hardware.