We experimentally investigated a single-qubit quantum classifier implemented on a silicon photonic integrated circuit, focusing on its performance under photon-limited conditions. Using the Data Reuploading method with layer-wise optimization via Sequential Minimal Optimization (SMO), input data were encoded into the photonic circuit, and classification was performed based on output detection probabilities. Heralded single photons, generated via spontaneous four-wave mixing in a silicon waveguide, served as the input states. Even when the average number of photon samples per input was reduced to approximately two, the classifier achieved nearly 90\% accuracy, provided that the training dataset was sufficiently large. The experimental results were consistent with numerical simulations, which also indicated that performance at low sample sizes can be improved by increasing the size of the training dataset. These findings demonstrate that photonic quantum classifiers can operate effectively with very few photons, supporting their practical feasibility for resource-efficient quantum machine learning on integrated photonic platforms.
We experimentally investigated a single-qubit quantum classifier implemented on a silicon photonic integrated circuit, focusing on its performance under photon-limited conditions. Using the Data Reuploading method with layer-wise optimization via Sequential Minimal Optimization (SMO), input data were encoded into the photonic circuit, and classification was performed based on output detection probabilities. Heralded single photons, generated via spontaneous four-wave mixing in a silicon waveguide, served as the input states. Even when the average number of photon samples per input was reduced to approximately two, the classifier achieved nearly 90% accuracy, provided that the training dataset was sufficiently large. The experimental results were consistent with numerical simulations, which also indicated that performance at low sample sizes can be improved by increasing the size of the training dataset. These findings demonstrate that photonic quantum classifiers can operate effectively with very few photons, supporting their practical feasibility for resource-efficient quantum machine learning on integrated photonic platforms.
In a single qubit system, a universal quantum classifier can be realized using the data reuploading technique. In this study, we propose a new quantum classifier applying this technique to bosonic systems and successfully demonstrate it using a silicon-based photonic integrated circuit. We established a theory of quantum machine learning algorithm applicable to bosonic systems and implemented a programmable optical circuit combined with an interferometer. Learning and classification using part of the implemented optical quantum circuit with uncorrelated two photons resulted in a classification with a success probability of 94±0.8% in the proof of principle experiment. As this method can be applied to an arbitrary two-mode N-photon system, further development of optical quantum classifiers, such as extensions to quantum entangled and multiphoton states, is expected in the future.
In this work, we investigate the use of a quantum circuit as a binary classification model in the context of quantum machine learning. We call this model, binary quantum classifier.
First, we describe fundamental concepts of quantum computing and introduce the computational tool used: Qibo, an open-source framework for efficient quantum simulations and quantum hardware control. Then, we describe how to design a binary quantum classifier for the classification of images and small arrays of variables by showing how to input data in the circuit, defining a quantum circuit model Ansatz with trainable parameters and a loss function, and implementing multiple minimizers. We test our quantum classifier with two data sets. The first one is the MNIST data set which is composed of handwritten digits (reduced to only handwritten zeros and handwritten ones for binary classification). We study the behavior of different minimizers by increasing the number of layers of the Ansatz. The second data set represents two different high energy collisions that can occur at colliders such as LHC (CERN). Due to in-time proton-proton interactions known as pile-up, we distinguish two different data sets: "without pile-up" and "with pile-up". These collisions can be represented by images of size 32x32 or by six high-level variables that we call features. By increasing the size of the training data set and the number of layers of the Ansatz, we search for the best minimizer. Splitting the data set in training set and test set, we compute: ROC curve, AUC score, confusion matrices and test set accuracy. For "with pile-up" images, we compare the results obtained with the quantum classifier with a small convolutional neural network.
We conclude that is possible to build a binary quantum classifier with a quantum circuit and we highlight its performances and limitations in comparison with classical technologies.
Abstract Hybrid quantum machine learning combines classical minimization with parameterized quantum circuits, enabling powerful learning models even on near-term quantum hardware. This work presents an evaluation of hybrid quantum machine learning classifiers using the data re-uploading framework across nine binary and multi-class classification tasks with varying geometric complexity. We compare three quantum circuit architectures, single-qubit, two-qubit, and two-qubit entangled, trained with three classical minimizers: COBYLA, Nelder-Mead, and SLSQP. Our experiments span training sizes from 1 to 200 samples and reveal that two-qubit classifiers, when paired with the SLSQP minimizer, achieve the highest overall test accuracy of 99.775% on structured tasks and strong performance (up to 89.78%) on complex multi-class pattern. Among minimizers, SLSQP consistently provides the best generalization, while entanglement improves accuracy in non-linear and fragmented tasks. By analyzing accuracy trends, generalization gaps, and confusion matrices, this study offers practical guidance for designing quantum classifiers that scale effectively and generalize well, providing a foundation for real-world Hybrid quantum machine learning applications.
In the current era, known as Noisy Intermediate-Scale Quantum (NISQ), encoding large amounts of data in the quantum devices is challenging and the impact of noise significantly affects the quality of the obtained results. A viable approach for the execution of quantum classification algorithms is the introduction of a well-known machine learning paradigm, namely, the ensemble methods. Indeed, the ensembles combine multiple internal classifiers, which are characterized by compact sizes due to the smaller data subsets used for training, to achieve more accurate and robust prediction performance. In this way, it is possible to reduce the qubit requirements with respect to a single larger classifier while achieving comparable or improved performance. In this work, we present an implementation and an extensive empirical evaluation of ensembles of quantum instance-based classifiers for binary classification, with the purpose of providing insights into their effectiveness, limitations, and potential for enhancing the performance of basic quantum models. In particular, three classical ensemble methods and three quantum instance-based classifiers have been taken into account here. Hence, the scheme that has been implemented (in Python) has a hybrid nature. The results (obtained on real-world datasets) have shown an accuracy advantage for the ensemble techniques with respect to the single quantum classifiers, and also an improvement in robustness. In fact, ensembles have proven effective not only in mitigating unsuitable data normalizations but also in reducing the impact of noise on quantum classifiers, enhancing their stability.
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.
Sequential minimum optimization is a machine learning global search training algorithm. It is applicable when the functional dependence of the cost function on a tunable parameter given the other parameters can be cheaply determined. This assumption is satisfied by quantum circuits built of known gates. We apply it to photonic circuits where the additional challenge appears: low frequency of coincidence events lowers the speed of the algorithm. We propose to modify the algorithm such that small sample size estimators are enough to successfully run the machine learning task. We demonstrate the effectiveness of the modified algorithm applying it to a photonic classifier with data reuploading.