Abstract One-class classification (OCC) is a fundamental problem in pattern recognition with a wide range of applications. This work presents a semi-supervised quantum machine learning algorithm for such a problem, which we call a variational quantum one-class classifier (VQOCC). The algorithm is suitable for noisy intermediate-scale quantum computing because the VQOCC trains a fully-parameterized quantum autoencoder with a normal dataset and does not require decoding. The performance of the VQOCC is compared with that of the one-class support vector machine (OC-SVM), the kernel principal component analysis (PCA), and the deep convolutional autoencoder (DCAE) using handwritten digit and Fashion-MNIST datasets. The numerical experiment examined various structures of VQOCC by varying data encoding, the number of parameterized quantum circuit layers, and the size of the latent feature space. The benchmark shows that the classification performance of VQOCC is comparable to that of OC-SVM and PCA, although the number of model parameters grows only logarithmically with the data size. The quantum algorithm outperformed DCAE in most cases under similar training conditions. Therefore, our algorithm constitutes an extremely compact and effective machine learning model for OCC.
Abstract One-class classification (OCC) is a fundamental problem in pattern recognition with a wide range of applications. This work presents a semi-supervised quantum machine learning algorithm for such a problem, which we call a variational quantum one-class classifier (VQOCC). The algorithm is suitable for noisy intermediate-scale quantum computing because the VQOCC trains a fully-parameterized quantum autoencoder with a normal dataset and does not require decoding. The performance of the VQOCC is compared with that of the one-class support vector machine (OC-SVM), the kernel principal component analysis (PCA), and the deep convolutional autoencoder (DCAE) using handwritten digit and Fashion-MNIST datasets. The numerical experiment examined various structures of VQOCC by varying data encoding, the number of parameterized quantum circuit layers, and the size of the latent feature space. The benchmark shows that the classification performance of VQOCC is comparable to that of OC-SVM and PCA, although the number of model parameters grows only logarithmically with the data size. The quantum algorithm outperformed DCAE in most cases under similar training conditions. Therefore, our algorithm constitutes an extremely compact and effective machine learning model for OCC.
Quantum machine learning has emerged as a promising frontier, leveraging the principles of quantum computing to enhance classical algorithms. This paper proposes an optimized Quantum Support Vector Classifier (QSVC) for the classification of the MNIST dataset (a benchmark in handwritten digit recognition). We employ a Chebyshev Parameterized Quantum Circuit (PQC) with an increased number of qubits and layers, and utilize an existing projected quantum kernel method to effectively capture the complex patterns in the data. To enhance model robustness, data augmentation techniques are applied, and dimensionality reduction is performed using Principal Component Analysis (PCA). The proposed QSVC demonstrates competitive accuracy on both the training and testing datasets, highlighting the potential of quantum kernel methods in practical machine learning applications. A comparative analysis with classical Support Vector Machines (SVM) demonstrates the feasibility of quantum methods for high-dimensional classification tasks. Additionally, we investigate the impact of varying the number of qubits in the quantum circuit, providing in-depth insights into the scalability and performance trade-offs of quantum kernel methods.
Quantum machine learning has the potential to provide powerful algorithms for artificial intelligence. The pursuit of quantum advantage in quantum machine learning is an active area of research. For current noisy intermediate-scale quantum computers, various quantum-classical hybrid algorithms have been proposed. One such previously proposed hybrid algorithm is a gate-based variational embedding classifier, which is composed of a classical neural network and a parameterized gate-based quantum circuit. We propose a quantum variational embedding classifier based on an analog quantum computer, where control signals vary continuously in time: our particular focus is an implementation using quantum annealers. In our algorithm, the classical data are transformed into the parameters of the time-varying Hamiltonian of the analog quantum computer by a linear transformation. The nonlinearity needed for a nonlinear classification problem is purely provided by the analog quantum computer through the nonlinear dependence of the final quantum state on the control parameters of the Hamiltonian. We perform numerical simulations that demonstrate the effectiveness of our algorithm for performing binary and multiclass classification on linearly inseparable datasets such as concentric circles and MNIST digits. Our classifier can reach accuracy comparable with that of the best classical classifiers. We find that the performance of our classifier can be increased by increasing the number of qubits, until the performance saturates and fluctuates. Moreover, the number of optimization parameters of our classifier scales linearly with the number of qubits. The increase of the number of training parameters when the size of our model increases is therefore not as fast as that of a neural network. Our algorithm presents the possibility of using current quantum annealers for solving practical machine-learning problems, and it could also be useful to explore quantum advantage in quantum machine learning.
One-class classification (OCC) is a fundamental problem in machine learning with numerous applications, such as anomaly detection and quality control. With the increasing complexity and dimensionality of modern datasets, there is a growing demand for advanced OCC techniques with better expressivity and efficiency. We introduce Neural Quantum Support Vector Data Description (NQSVDD), a classical-quantum hybrid framework for OCC that performs end-to-end optimized hierarchical representation learning. NQSVDD integrates a classical neural network with trainable quantum data encoding and a variational quantum circuit, enabling the model to learn nonlinear feature transformations tailored to the OCC objective. The hybrid architecture maps input data into an intermediate high-dimensional feature space and subsequently projects it into a compact latent space defined through quantum measurements. Importantly, both the feature embedding and the latent representation are jointly optimized such that normal data form a compact cluster, for which a minimum-volume enclosing hypersphere provides an effective decision boundary. Experimental evaluations on benchmark datasets demonstrate that NQSVDD achieves competitive or superior AUC performance compared to classical Deep SVDD and quantum baselines, while maintaining parameter efficiency and robustness under realistic noise conditions.
Quantum computer introduces a novel approach to process information. In quantum information processing, the law of quantum mechanics is applied to solve many practical computational problems. Classification is one such problem that can be resolved efficiently with the gate model quantum computer. There are several types of classifiers available in quantum domain, such as- variational quantum classifier (VQC), Quantum Support Vector Machine (QSVM) with Kernel Approximation, Hybrid Quantum Neural Network (QNN) etc. However, in this study, the mathematical similarities between VQC and classical support vector machine (SVM) and the components of the VQC are analyzed to optimize the performance of the classifier. For the convenience of the study, publicly available datasets, such as- IRIS dataset and Breast cancer dataset, are used in the experiments. IRIS dataset is brought into play for the testing and breast cancer dataset dimension reduced by Principle component analysis (PCA) is for validity test of the optimized VQC. After studying the VQC components in detail, it is found that the optimized VQC outperforms some of the classical machine learning algorithms or sometimes works as similar as classical SVM. The optimized VQC algorithm classifies IRIS dataset with 100% of accuracy and PCA dimension reduced Breast cancer dataset with 90% of accuracy. All of these studies are conducted with the help of Qiskit- an open-source software development kit (SKD) which is developed by IBM. So, the quantum device is considered to be ideal in every experiment.
Classification of quantum data is essential for quantum machine learning and near-term quantum technologies. In this paper, we propose a new hybrid quantum-classical framework for supervised quantum learning, which we call Variational Shadow Quantum Learning (VSQL). Our method in particular utilizes the classical shadows of quantum data, which fundamentally represent the side information of quantum data with respect to certain physical observables. Specifically, we first use variational shadow quantum circuits to extract classical features in a convolution way and then utilize a fully-connected neural network to complete the classification task. We show that this method could sharply reduce the number of parameters and thus better facilitate quantum circuit training. Simultaneously, less noise will be introduced since fewer quantum gates are employed in such shadow circuits. Moreover, we show that the Barren Plateau issue, a significant gradient vanishing problem in quantum machine learning, could be avoided in VSQL. Finally, we demonstrate the efficiency of VSQL in quantum classification via numerical experiments on the classification of quantum states and the recognition of multi-labeled handwritten digits. In particular, our VSQL approach outperforms existing variational quantum classifiers in the test accuracy in the binary case of handwritten digit recognition and notably requires much fewer parameters.
In order to leverage quantum computers for machine learning tasks such as image classification, consideration is required. Noisy Intermediate-Scale Quantum (NISQ) computers have limitations that include noise, scalability, read-in and read-out times, and gate operation times. Therefore, strategies should be devised to mitigate the impact complex datasets that can have on the overall efficiency of a quantum machine learning pipeline. This may otherwise lead to excessive resource demands or noise. We apply a classical feature extraction using a ResNet10-inspired convolutional autoencoder to reduce dataset dimensionality and extract abstract, meaningful features before feeding them into a quantum layer. The chosen quantum layer is a quantum-enhanced support vector machine (QSVM), as SVMs typically do not require large sample sizes to identify patterns in data and have short-depth quantum circuits, which limits the impact of noise. The autoencoder is trained to extract meaningful features through image reconstruction, aiming to minimize the mean squared error across a training set of images. We use three datasets to illustrate the pipeline: HTRU-1, MNIST, and CIFAR-10. We include a quantum-enhanced one-class support vector machine (QOCSVM) for the highly unbalanced HTRU-1 set, with classical machine learning results for comparison. HTRU-2 is also included to serve as a benchmark for a dataset with meaningful features. The autoencoder achieved near-perfect reconstruction and high accuracy for MNIST, while CIFAR-10 showed poorer performance due to image complexity, and HTRU-1 struggled due to the imbalance in the dataset. The varying performance across datasets highlights the need to balance dimensionality reduction and prediction performance using quantum methods.