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arXiv:2511.21951

A scalable advantage in multi-photon quantum machine learning

Yong Wang, Zhenghao Yin, Tobias Haug, Ciro Pentangelo, Simone Piacentini, Andrea Crespi, Francesco Ceccarelli, Roberto Osellame, Philip Walther

quant-phphysics.opticsSubmitted Nov 26, 2025• Announced Nov 28, 2025• 0 citations
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Abstract

Photons are promising candidates for quantum information technology due to their high robustness and long coherence time at room temperature. Inspired by the prosperous development of photonic computing techniques, recent research has turned attention to performing quantum machine learning on photonic platforms. Although photons possess a high-dimensional quantum feature space suitable for computation, a general understanding of how to harness it for learning tasks remains blank. Here, we establish both theoretically and experimentally a scalable advantage in quantum machine learning with multi-photon states. Firstly, we prove that the learning capacity of linear optical circuits scales polynomially with the photon number, enabling generalization from smaller training datasets and yielding lower test loss values. Moreover, we experimentally corroborate these findings through unitary learning and metric learning tasks, by performing online training on a fully programmable photonic integrated platform. Our work highlights the potential of photonic quantum machine learning and paves the way for achieving quantum enhancement in practical machine learning applications.

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Photons are promising candidates for quantum information technology due to their high robustness and long coherence time at room temperature. Inspired by the prosperous development of photonic computing techniques, recent research has turned attention to performing quantum machine learning on photonic platforms. Although photons possess a high-dimensional quantum feature space suitable for computation, a general understanding of how to harness it for learning tasks remains blank. Here, we establish both theoretically and experimentally a scalable advantage in quantum machine learning with multi-photon states. Firstly, we prove that the learning capacity of linear optical circuits scales polynomially with the photon number, enabling generalization from smaller training datasets and yielding lower test loss values. Moreover, we experimentally corroborate these findings through unitary learning and metric learning tasks, by performing online training on a fully programmable photonic integrated platform. Our work highlights the potential of photonic quantum machine learning and paves the way for achieving quantum enhancement in practical machine learning applications.
Abstract Photons are promising candidates for quantum information technology due to their high robustness and long coherence time at room temperature. Inspired by recent advances in photonic computing techniques, research has increasingly turned to quantum machine learning (QML) on photonic platforms. Although photons provide a high-dimensional quantum feature space suitable for computation, a general understanding of how photon number can be harnessed for learning tasks remains limited. Here, we establish both theoretically and experimentally a learning-capacity advantage of multi-photon states over single-photon states in photonic QML. We prove that the learning capacity of linear optical circuits, quantified by the rank of the data quantum Fisher information matrix, scales polynomially with the photon number. This scaling enables multi-photon models to generalize from fewer training states than corresponding single-photon models and to achieve lower test loss under the same architecture and learning protocol. Moreover, we experimentally corroborate these findings through unitary learning and metric learning tasks, by performing online training on a fully programmable photonic integrated platform. Our work highlights the potential of photonic QML and paves the way for achieving quantum enhancement in practical machine learning applications.
Recent advancements in machine learning have led to an exponential increase in computational demands, driving the need for innovative computing platforms. Quantum computing, with its Hilbert space scaling exponentially with the number of particles, emerges as a promising solution. In this work, we implement a quantum extreme machine learning (QELM) protocol leveraging indistinguishable photon pairs and multimode fiber as a random densly connected layer. We experimentally study QELM performance based on photon coincidences -- for distinguishable and indistinguishable photons -- on an image classification task. Simulations further show that increasing the number of photons reveals a clear quantum advantage. We relate this improved performance to the enhanced dimensionality and expressivity of the feature space, as indicated by the increased rank of the feature matrix in both experiment and simulation.
Photonic Quantum Machine Learning (PQML) is an emerging method to implement scalable, energy-efficient quantum information processing by combining photonic quantum computing technologies with machine learning techniques. The features of photonic technologies offer several benefits: room-temperature operation; fast (low delay) processing of signals; and the possibility of representing computations in high-dimensional (Hilbert) spaces. This makes photonic technologies a good candidate for the near-term development of quantum devices. However, noise is still a major limiting factor for the performance, reliability, and scalability of PQML implementations. This review provides a detailed and systematic analysis of the sources of noise that will affect PQML implementations. We will present an overview of the principal photonic quantum computer designs and summarize the many different types of quantum machine learning algorithms that have been successfully implemented using photonic quantum computer architectures such as variational quantum circuits, quantum neural networks, and quantum support vector machines. We identify and categorize the primary sources of noise within photonic quantum systems and how these sources of noise behave algorithm-specifically with respect to degrading the accuracy of learning, unstable training, and slower convergence than expected. Additionally, we review traditional and advanced techniques for characterizing noise and provide an extensive survey of strategies for mitigating the effects of noise on learning performance. Finally, we discuss recent advances that demonstrate PQML's capability to operate in real-world settings with realistic noise conditions and future obstacles that will challenge the use of PQML as an effective quantum processing platform.
Recent photonic quantum machine learning proposals combined linear optics with adaptivity to enhance expressivity and improve algorithm performance and scalability. The particle-number-preserving property of linear optical platforms was recently employed to design a quantum convolutional neural network architecture with advantages in terms of resource complexity and the number of parameters needed. Here, we design and experimentally implement a photonic quantum convolutional neural network (PQCNN) based on linear optics equipped with adaptive state injection, a tool that increases the linear optical circuits controllability. We validate the PQCNN for a binary image classification on a photonic platform utilizing a semiconductor quantum dot-based single-photon source and programmable integrated photonic interferometers comprising 8 and 12 modes. To investigate the scalability of the PQCNN design, we performed numerical simulations on datasets of different sizes. These findings demonstrate potential utilities of a simple adaptive technique for a nonlinear boson sampling task, compatible with near-term quantum devices.
Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require significant resources for variational parameter optimization and face issues with vanishing gradients, leading to experiments that are either limited in scale or lack potential for quantum advantage. To address this, we develop a general-purpose, gradient-free, and scalable quantum reservoir learning algorithm that harnesses the quantum dynamics of neutral-atom analog quantum computers to process data. We experimentally implement the algorithm, achieving competitive performance across various categories of machine learning tasks, including binary and multi-class classification, as well as timeseries prediction. Effective and improving learning is observed with increasing system sizes of up to 108 qubits, demonstrating the largest quantum machine learning experiment to date. We further observe comparative quantum kernel advantage in learning tasks by constructing synthetic datasets based on the geometric differences between generated quantum and classical data kernels. Our findings demonstrate the potential of utilizing classically intractable quantum correlations for effective machine learning. We expect these results to stimulate further extensions to different quantum hardware and machine learning paradigms, including early fault-tolerant hardware and generative machine learning tasks.
The implementation of large-scale universal quantum computation represents a challenging and ambitious task on the road to quantum processing of information. In recent years, an intermediate approach has been pursued to demonstrate quantum computational advantage via non-universal computational models. A relevant example for photonic platforms has been provided by the Boson Sampling paradigm and its variants, which are known to be computationally hard while requiring at the same time only the manipulation of the generated photonic resources via linear optics and detection. Beside quantum computational advantage demonstrations, a promising direction towards possibly useful applications can be found in the field of quantum machine learning, considering the currently almost unexplored intermediate scenario between non-adaptive linear optics and universal photonic quantum computation. Here, we report the experimental implementation of quantum machine learning protocols by adding adaptivity via post-selection to a Boson Sampling platform based on universal programmable photonic circuits fabricated via femtosecond laser writing. Our experimental results demonstrate that Adaptive Boson Sampling is a viable route towards dimension-enhanced quantum machine learning with linear optical devices. Extending quantum photonics’ capabilities from simple linear-optics-based schemes to universal quantum computing presents several challenges, but intermediate regimes with some degree of adaptivity might already bring practical advantages. Here, the authors experimentally emulate an adaptive Boson Sampling scheme using post-selection, and apply it to a data classification task.