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arXiv:2404.15266 · Communications Physics

Quantum optical classifier with superexponential speedup

Simone Roncallo, Angela Rosy Morgillo, Chiara Macchiavello, Lorenzo Maccone, Seth Lloyd

Published Apr 10, 2025• 5 citations
arXivHTMLPDF

Abstract

Abstract Classification is a central task in deep learning algorithms. Usually, images are first captured and then processed by a sequence of operations, of which the artificial neuron represents one of the fundamental units. This paradigm requires significant resources that scale (at least) linearly in the image resolution, both in terms of photons and computational operations. Here, we present a quantum optical pattern recognition method for binary classification tasks. It classifies objects without reconstructing their images, using the rate of two-photon coincidences at the output of a Hong-Ou-Mandel interferometer, where both the input and the classifier parameters are encoded into single-photon states. Our method exhibits the behaviour of a classical neuron of unit depth. Once trained, it shows a constant $${{\mathcal{O}}}(1)$$ O ( 1 ) complexity in the number of computational operations and photons required by a single classification. This is a superexponential advantage over a classical artificial neuron.

DOI
10.1038/s42005-025-02020-5

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We present a quantum optical pattern recognition method for binary classification tasks. Without direct image reconstruction, it classifies an object in terms of the rate of two-photon coincidences at the output of a Hong-Ou-Mandel interferometer, where both the input and the classifier parameters are encoded into single-photon states. Our method exhibits the same behaviour of a classical neuron of unit depth. Once trained, it shows a constant O(1)\mathcal{O}(1)O(1) complexity in the number of computational operations and photons required by a single classification. This is a superexponential advantage over a classical neuron (that is at least linear in the image resolution). We provide simulations and analytical comparisons with analogous neural network architectures.
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.
Machine learning is a powerful tool which, when given the availability of comprehensive datasets, required training iterations and the necessary resources to support them, can achieve impressive results in a variety of classification tasks. In this paper, we put forward a quantum alternative for users that do not posses the ability to gather and store large amounts of data to be used subsequently in lengthy training iterations. A light-weight probabilistic quantum binary classifier can be built by encoding the two chosen class representatives (images) into quantum vectors, such that a Principal Component decomposition can express the differences between them only along one dimension (basis vector). A standard measurement in the computational basis will then project any transformed input sample along one of the two classes. The classifier accepts quantum representations of images as input, which require exponentially fewer number of quantum bits compared with the number of classical bits used to store an image. The technique is illustrated on a "proof of concept" example, in which a quantum character recognizer is built to label any input sample image as either letter {\bf A} or {\bf P}. The quantum classifier can be tuned to "favor" any of the two classes and the measurement probabilities follow closely how far an input sample is from the two class representatives. Despite its relative simplicity, the quantum classifier can distinguish between the standard letter {\bf A} and the standard letter {\bf P} with 98%98\%98% accuracy. In principle, the procedure can be applied to any image classification task, including gray-scale and color images, as well as classification problems in which an input sample is characterized by a collection of properties given by their values.
Abstract Classical shallow networks are universal approximators. Given a sufficient number of neurons, they can reproduce any continuous function to arbitrary precision, with a resource cost that scales linearly in both the input size and the number of trainable parameters. In this work, we present a quantum optical protocol that implements a shallow network with an arbitrary number of neurons. Both the input data and the parameters are encoded into single-photon states. Leveraging the Hong–Ou–Mandel effect, the network output is determined by the coincidence rates measured when the photons interfere at a beam splitter, with multiple neurons prepared as a mixture of single-photon states. Remarkably, once trained, our model requires constant optical resources regardless of the number of input features and neurons.
Abstract A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and have a lower variance than the individual classifiers that make them up, but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log ( B ) operations. This implies an exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively to the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.
A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and lower variance than the individual classifiers that make them up but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain BBB transformations of the quantum state which encodes the training set in only log(B)log\left(B\right)log(B) operations. This implies exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.