Quantum Optical Neuron for Image Classification via Multiphoton Interference

Abstract

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.

Figures (7)

• Figure 1: QON and QOSN scheme. The core of the QON operation is Hong-Ou-Mandel (HOM) interference between two spatially modulated photons. The input photon (green profile) carries the spatial information of the image to be classified, while the probe photon encodes the model weights. The neuron's weighted sum is physically implemented via the HOM interference. Bucket detectors provide the HOM visibility, which, combined with a trainable bias, serves as the input for a sigmoid activation function predicting the input image's class.
• Figure 2: Experimental setup characterization. Panel (a) illustrates the schematic of the experimental setup used to implement the QON. Pairs of single photons, initialized in the $TEM_{00}$ spatial mode, are modulated by spatial light modulators (SLMs) to generate arbitrary transverse amplitude profiles at the beam-splitter plane. Following interference at the beam-splitter, the photons are coupled into multimode fibers to measure coincidence counts and, ultimately, determine the Hong-Ou-Mandel (HOM) visibility. In panels (b)-(h), we report the characterization of the HOM interference for different spatial profiles, obtained by measuring coincidence counts as a function of the relative time delay between photons. In panel (b), we consider the case of Gaussian profiles (illustrated in the inset), which yield an HOM visibility of ($84.5 \pm 2.4$)%. Panels (c)-(d) and (e)-(f) show the results of spatial modulation applied to a coherent beam for example images from the MNIST and Fashion-MNIST datasets, respectively, with target images shown in the insets. Panel (g) displays the HOM dips resulting from the combinations of MNIST "0-0" and "0-1" images, while panel (h) considers combinations of "t-shirt--t-shirt" and "t-shirt--sneaker" from the Fashion-MNIST dataset.
• Figure 3: QON and QOSN performance. Panels (a)-(b) and (e)-(f) display the evolution of training accuracy and loss over the training epochs. Panels (a)-(b) correspond to the classification of MNIST "0" vs. "1" images (20 epochs), while panels (e)-(f) correspond to Fashion-MNIST "sneaker" vs. "bag" images (30 epochs). Blue markers represent the single QON performance, while red markers indicate the results obtained with a two-neuron QOSN. The errorbars reported in panels (a)-(b) and (e)-(f) correspond to the standard deviation achieved on 100 independent random choices of 50-sample subsets of the training set onto which the accuracies and loss have been evaluated. Panels (c)-(d) and (g)-(h) report the confusion matrices evaluated on the test datasets for MNIST and Fashion-MNIST, respectively. In particular, panels (c) and (g) show the results for the single QON, while panels (d) and (h) correspond to the two-neuron QOSN.
• Figure 4: HOM visibilities during the model training Panels (a)-(d) illustrate representative examples of QON weights during the training, reporting, in particular, their profiles at epochs 0, 2, 10, and 20. In panel (e), we report the evolution of the measured HOM visibilities averaged on the train dataset, separated for instances of MNIST images of zeros (green solid line and shaded area) and ones (orange solid line and shaded area). The red dashed line represents the learned threshold for which the model performs the binary classification, obtained as 0.5-$b_i$, where $b_i$ represents the current epoch bias. Panel (f) illustrates the correspondence between the final average and standard deviation of the visibilities for the two classes and the final prediction obtained as the output of the sigmoid activation function (black solid line). Dots in different shades of green and orange illustrate the average biased visibilities of "0" and "1" MNIST samples, respectively, at epochs 0, 2, 10, and 20.
• Figure 5: QON performances with variable resolution. Panels (a)-(d) illustrate a representative example of an MNIST image at different resolutions, i.e., $9\times9$, $16\times16$, $32\times32$, and $64\times64$ pixels, while the central row of panels (e)-(h) shows the corresponding trained weights profiles. In panel(i), we report the training and test accuracies achieved using image datasets of varying resolutions. The error bars represent half the maximum variation observed over the final 10 epochs, capturing the fluctuations after the accuracies have converged.