Abstract One of the fastest growing areas of interest in quantum computing is its use within machine learning methods, in particular through the application of quantum kernels. Despite this large interest, there exist very few proposals for relevant physical platforms to evaluate quantum kernels. In this article, we propose and simulate a protocol capable of evaluating quantum kernels using Hong–Ou–Mandel interference, an experimental technique that is widely accessible to optics researchers. Our proposal utilises the orthogonal temporal modes of a single photon, allowing one to encode multi-dimensional feature vectors. As a result, interfering two photons and using the detected coincidence counts, we can perform a direct measurement and binary classification. This physical platform confers an exponential quantum advantage also described theoretically in other works. We present a complete description of this method and perform a numerical experiment to demonstrate a sample application for binary classification of classical data.
Abstract One of the fastest growing areas of interest in quantum computing is its use within machine learning methods, in particular through the application of quantum kernels. Despite this large interest, there exist very few proposals for relevant physical platforms to evaluate quantum kernels. In this article, we propose and simulate a protocol capable of evaluating quantum kernels using Hong–Ou–Mandel interference, an experimental technique that is widely accessible to optics researchers. Our proposal utilises the orthogonal temporal modes of a single photon, allowing one to encode multi-dimensional feature vectors. As a result, interfering two photons and using the detected coincidence counts, we can perform a direct measurement and binary classification. This physical platform confers an exponential quantum advantage also described theoretically in other works. We present a complete description of this method and perform a numerical experiment to demonstrate a sample application for binary classification of classical data.
The rapid growth of machine learning is increasingly constrained by the energy and bandwidth limits of classical hardware. Optical and quantum technologies offer an alternative route, enabling high-dimensional, parallel information processing directly in the physical layer, particularly suited for imaging tasks. In this context, quantum photonic platforms provide both a natural mechanism for computing inner products and a promising path to energy-efficient inference in photon-limited regimes. Here, we experimentally demonstrate a camera-free quantum-optical images classifier that performs inference directly at the measurement layer using Hong-Ou-Mandel (HOM) interference of spatially programmable single photons. Two-photon coincidences directly report the overlap between an input image mode and a learned template, replacing pixel-resolved acquisition with a single global measurement. We realize both a single-perceptron quantum optical neuron and a two-neuron shallow network, achieving high accuracy on benchmark datasets with strong robustness to experimental noise and minimal hardware complexity. With a fixed measurement budget, performance remains insensitive to input resolution, demonstrating intrinsic robustness to the number of pixels, which would be impossible in a classical framework. This approach paves the way toward neuromorphic quantum photonic processors capable of extracting task-relevant information directly from HOM interference, with promising applications in remote object recognition, low-signal sensing, and photon-starved biological microscopy.
Multiphoton interference represents one of the key features in photonic platforms for quantum communication, quantum simulation, quantum computing and quantum sensing. Starting from the first two-photon experiment by Hong-Ou-Mandel [1], it has been shown that multiphoton interference lies at the heart of computational complexity in linear optical interferometers, the most notable example being provided by the Boson Sampling model [2]. This model corresponds to sampling from the evolution of n indistinguishable photons in a multimode linear network, and has been shown to be hard to simulate classicaly thus representing a promising route to experimentally reach the quantum advantage regime. It has been shown, however, that genuine multiparticle interference is necessary for high computational complexity. Hence, appropriate methods for detection of such feature should be developed since the complexity of problem prevents the application of trivial methods.
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.
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed quantum states encoding the training data, while the model training is processed on a classical computer. Our two-photon proposal encodes data points in a discrete, eight-dimensional feature Hilbert space. In order to maximize the application range of the deployable kernels, we optimize feature maps towards the resulting kernels' ability to separate points, i.e., their "resolution," under the constraint of finite, fixed Hilbert space dimension. Implementing these kernels, our setup delivers viable decision boundaries for standard nonlinear supervised classification tasks in feature space. We demonstrate such kernel-based quantum machine learning using specialized multiphoton quantum optical circuits. The deployed kernel exhibits exponentially better scaling in the required number of qubits than a direct generalization of kernels described in the literature.
Abstract Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by engineering the quantum interference effect to carry out the kernel evaluation in parallel. For practical applications of these quantum machine learning methods, an important issue is to minimize the size of quantum circuits. We present the simplest quantum circuit for constructing a kernel-based binary classifier. This is achieved by generalizing the interference circuit to encode data labels in the relative phases of the quantum state and by introducing compact amplitude encoding, which encodes two training data vectors into one quantum register. When compared to the simplest known quantum binary classifier, the number of qubits is reduced by two and the number of steps is reduced linearly with respect to the number of training data. The two-qubit measurement with post-selection required in the previous method is simplified to single-qubit measurement. Furthermore, the final quantum state has a smaller amount of entanglement than that of the previous method, which advocates the cost-effectiveness of our method. Our design also provides a straightforward way to handle an imbalanced data set, which is often encountered in many machine learning problems.
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 γ, 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 5×107 circuits at n = 10,000. Protocol variance is thus sufficient to explain the field's contradictory conclusions.