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.
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.
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.
Quantum neural networks (QNNs) have shown promise in leveraging quantum computation for machine learning tasks. Utilizing multiple identical photons as input, multi-photon quantum neural networks (MPQNNs) have the potential to enhance the expressivity through increasing the photon number. However, how precisely the expressivity of an MPQNN is affected by an increase in photon number, and whether it can be infinitely enhanced by increasing the photon number, remains unexplored. In this work, we quantitatively estimate the expressivity of this model by deriving upper bounds on approximation error in two cases. In the case of a fixed observable, there exists a threshold that scales linearly with the mode number. Below the threshold, the expressivity of an MPQNN can be enhanced polynomially by increasing the photon number. Above the threshold, however, increasing the photon number does not affect the expressivity. In the case of a trainable observable, the expressivity can always be enhanced polynomially by increasing the photon number. These findings are then validated by numerical simulations. Our work elucidates the performance enhancement of multi-photon quantum feature in QNNs, as well as its limitations, offering guidance for leveraging multi-photon advantages in quantum machine learning.
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.
Abstract The rapid advancement of artificial intelligence has made machine learning (ML) methods central to modern science, technology, and industry. At the same time, the emergence of programmable quantum computers, along with the anticipation of large-scale fault-tolerant machines in the future, has generated interest in the potential of quantum machine learning (QML)—a field that explores quantum properties to enhance ML tasks. While QML is often considered a promising application for quantum computing, its practical advantages over classical methods remain an area of active research and exploration. In recent years, QML has garnered significant global attention, with researchers investigating its potential and limitations. In this chapter, we introduce the fundamentals of QML and provide an overview of recent developments and future trends in the field. We outline potential opportunities where quantum properties might offer advantages in ML tasks while also addressing the open challenges that QML faces in terms of scalability, implementation, and practical utility. We also explore the potential applications of QML in defense and security-sensitive domains. Here, researchers speculate that integrating quantum computing into ML could lead to the development of systems capable of resisting sophisticated threats, such as data manipulation and poisoning. However, realizing these possibilities requires further advancements in both quantum hardware and algorithmic design, making QML a promising yet still evolving field.
Quantum machine learning (QML) is an emerging research area that combines quantum computation with classical machine learning (ML). The primary objective of QML is to enhance the performance of traditional ML algorithms by harnessing quantum phenomena. Inspired by the success of classical neural networks (NNs), their quantum analog, commonly known as quantum neural networks (QNNs), are widely being investigated. Despite the significant interest, the literature still lacks some concrete evidence about QNN's superiority over their classical counterparts, especially in practical applications. This paper empirically demonstrates a greater capacity in hybrid quantum neural networks (HQNNs) for a practical application, namely multi-class classification. In particular, we train both the HQNNs and their equivalent classical counterparts on the same data. We then benchmark the models' accuracy for quantifying model's capacity, where greater accuracy typically implies greater capacity. The results demonstrate a clear quantum advantage, i.e., greater capacity of HQNNs over their classical counterparts, where the HQNN models constantly achieve better accuracy. This superiority in performance by HQNNs serves as a foundational study for further investigation to magnify the quantum advantage in real-world applications of HQNNs.