Hybrid Boson Sampling-Neural Network Architecture for Enhanced Classification

TL;DR

This work addresses the challenge of achieving practical quantum advantage in machine learning by coupling a classical neural network with a programmable boson-sampling circuit to form a quantum kernel for SVM classification. The hybrid framework enables data to be compressed into a feature space mapped by a photonic quantum circuit, whose kernel improves class separation in a high-dimensional Hilbert space. Across four datasets, the boson-sampling–based kernel outperforms classical linear and sigmoid kernels, and its performance scales with the number of photons and modes, suggesting a viable path toward quantum-enhanced learning on near-term hardware. The study also analyzes practical considerations, including readout reductions and kernel estimation noise, underscoring the method's feasibility on current photonic platforms and outlining avenues for architectural and encoding enhancements.

Abstract

Demonstration of quantum advantage for classical machine learning tasks remains a central goal for quantum technologies and artificial intelligence. Two major bottlenecks to this goal are the high dimensionality of practical datasets and limited performance of near-term quantum computers. Boson sampling is among the few models with experimentally verified quantum advantage, yet it lacks practical applications. Here, we develop a hybrid framework that combines the computational power of boson sampling with the adaptability of neural networks to construct quantum kernels that enhance support vector machine classification. The neural network adaptively compresses the data features onto a programmable boson sampling circuit, producing quantum states that span a high-dimensional Hilbert space and enable improved classification performance. Using four datasets with various classes, we demonstrate that our model outperforms classical linear and sigmoid kernels. These results highlight the potential of boson sampling-based quantum kernels for practical quantum-enhanced machine learning.

Figures (6)

• Figure 1: Schematic overview of the proposed model. (a) The input dataset is first processed by a neural network that reduces its features to match the number of tunable phase shifters (red rectangles) in the boson sampling circuit. Each kernel value for a pair of data points corresponds to the probability of coincidence detection at the circuit output. During training, the mean squared error between the estimated kernel values and the target pairwise label equivalence is used as the loss function to optimize the neural network parameters. After training, the computed kernel matrix is supplied to an SVM classifier to predict the labels of unseen test data. (b) Conceptually, the model learns to increase the quantum-state fidelity between samples of the same class while suppressing it for samples from different classes, thereby enhancing class discrimination in the Hilbert space representation.
• Figure 2: Mean test accuracy of the proposed model as a function of the number of indistinguishable photons. Results are presented for (a) Ionosphere, (b) Spambase, (c) MNIST, and (d) Fashion-MNIST datasets. The solid blue line denotes the average classification accuracy obtained using the hybrid quantum kernel for different photon numbers. Dashed lines correspond to the mean accuracy achieved with SVM using classical kernels, whereas the dotted curve shows the performance of the corresponding standalone classical neural network without any kernel integration. All values represent averages over five independent runs, with error bars indicating the standard deviation.
• Figure 3: Effect of (a) Hilbert space dimension and (b) number of modes and layers on the accuracy of MNIST classification. In panel (b), the red line indicates the minimum number of layers ($\ell{=}m{-}1$) required for full connectivity between the first and last modes. All results are averaged over five independent runs.
• Figure 4: Test accuracy of the model as a function of the number of training readout points for (a) Ionosphere, (b) Spambase, (c) MNIST, and (d) Fashion-MNIST datasets for different number of photons. Each point represents the average over five independent selections of random training and test data samples.
• Figure 5: Evolution of test accuracy during neural network training for (a) Ionosphere, (b) Spambase, (c) MNIST, and (d) Fashion-MNIST datasets.