Quantum machine learning (QML) has emerged as an important area for Quantum applications, although useful QML applications would require many qubits. Therefore our paper is aimed at exploring the successful application of the Quantum Support Vector Machine (QSVM) algorithm while balancing several practical and technical considerations under the Noisy Intermediate-Scale Quantum (NISQ) assumption. For the quantum SVM under NISQ, we use quantum feature maps to translate data into quantum states and build the SVM kernel out of these quantum states, and further compare with classical SVM with radial basis function (RBF) kernels. As data sets are more complex or abstracted in some sense, classical SVM with classical kernels leads to less accuracy compared to QSVM, as classical SVM with typical classical kernels cannot easily separate different class data. Similarly, QSVM should be able to provide competitive performance over a broader range of data sets including ``simpler'' data cases in which smoother decision boundaries are required to avoid any model variance issues (i.e., overfitting). To bridge the gap between ``classical-looking'' decision boundaries and complex quantum decision boundaries, we propose to utilize general shallow unitary transformations to create feature maps with rotation factors to define a tunable quantum kernel, and added regularization to smooth the separating hyperplane model. We show in experiments that this allows QSVM to perform equally to SVM regardless of the complexity of the data sets and outperform in some commonly used reference data sets.
Quantum machine learning (QML) has emerged as an important area for Quantum applications, although useful QML applications would require many qubits. Therefore our paper is aimed at exploring the successful application of the Quantum Support Vector Machine (QSVM) algorithm while balancing several practical and technical considerations under the Noisy Intermediate-Scale Quantum (NISQ) assumption. For the quantum SVM under NISQ, we use quantum feature maps to translate data into quantum states and build the SVM kernel out of these quantum states, and further compare with classical SVM with radial basis function (RBF) kernels. As data sets are more complex or abstracted in some sense, classical SVM with classical kernels leads to less accuracy compared to QSVM, as classical SVM with typical classical kernels cannot easily separate different class data. Similarly, QSVM should be able to provide competitive performance over a broader range of data sets including simpler'' data cases in which smoother decision boundaries are required to avoid any model variance issues (i.e., overfitting). To bridge the gap between classical-looking'' decision boundaries and complex quantum decision boundaries, we propose to utilize general shallow unitary transformations to create feature maps with rotation factors to define a tunable quantum kernel, and added regularization to smooth the separating hyperplane model. We show in experiments that this allows QSVM to perform equally to SVM regardless of the complexity of the data sets and outperform in some commonly used reference data sets.
Abstract Support vector machines (SVMs) are widely used for classification, but become computationally expensive as datasets grow and data become high-dimensional or nonlinearly separable. Quantum support vector machines (QSVMs) enhance the traditional SVMs by replacing conventional feature mappings with quantum-implemented embeddings that project data into high-dimensional Hilbert spaces, potentially improving expressive power and efficiency. However, training QSVMs on current noisy intermediate-scale quantum (NISQ) devices remains challenging, as constructing the quantum kernel matrix requires repeated circuit executions and scales quadratically with dataset size. We propose NQ-SVM , a hybrid quantum-classical method that incorporates the Nystr\"om approximation to enhance the scalability of QSVMs. By selecting a small set of landmark points, the Nystr\"om method yields a low-rank kernel approximation, reducing complexity from (O(n2)) to (O(nm)), while preserving the quantum advantages in handling high-dimensional, non-linear data. Extensive simulations demonstrate that NQ-SVM achieves comparable classification accuracy to classical SVMs and full QSVMs, while substantially reducing training time and kernel evaluation costs. These results underscore the potential of NQ-SVM as a scalable and practical hybrid framework for near-term quantum machine learning (QML).
Anomaly detection, an important task in data analysis, involves identifying observations or events that deviate in some way from the rest of the data. Machine learning techniques have shown success in automating this process by detecting hidden patterns and deviations in large-scale data. The potential of quantum computing for machine learning has been widely recognized, leading to extensive research efforts to develop suitable quantum machine learning (QML) algorithms. In particular, the search for QML algorithms for near-term NISQ devices is in full swing. However, NISQ devices pose additional challenges due to their limited qubit coherence times, low number of qubits, and high error rates. Kernel methods based on quantum kernel estimation have emerged as a promising approach to QML on NISQ devices, offering theoretical guarantees, versatility, and compatibility with NISQ constraints. Especially support vector machines (SVM) utilizing quantum kernel estimation have shown success in various supervised learning tasks. However, in the context of anomaly detection, semisupervised learning is of great relevance, and yet there is limited research published in this area. This paper introduces an approach to semisupervised anomaly detection based on the reconstruction loss of a support vector regression (SVR) with quantum kernel. This novel model is an alternative to the variational quantum and quantum kernel one-class classifiers, and is compared to a quantum autoencoder as quantum baseline and a SVR with radial-basis-function (RBF) kernel as well as a classical autoencoder as classical baselines. The models are benchmarked extensively on 10 real-world anomaly detection data sets and one toy data set and it is shown that our SVR model with quantum kernel performs better than the SVR with RBF kernel as well as all other models, achieving highest mean AUC over all data sets. In addition, our QSVR outperforms the Quantum autoencoder on 9 out of 11 data sets.
Quantum Machine Learning (QML) provides a pathway for analysing nonlinear relationships through quantum- enhanced feature spaces. Although quantum models are theoreti- cally well suited for high-complexity data, current hardware and simulator limitations restrict their use to small datasets. For this reason, the original large Web Phishing Detection Dataset was reduced to 200 representative samples through dimensionality reduction, allowing controlled experimentation and enabling evaluation of quantum behaviour with manageable computational cost. QML research commonly follows this approach, testing algorithms on small datasets first, because quantum feature maps can generate exponentially expressive Hilbert-space embeddings even from limited inputs. In this study, multiple Quantum Support Vector Machine (QSVM) models were implemented using fidelity-based quantum kernels and Pauli feature maps. Models with 2 to 10 qubits were evaluated to observe how circuit width affects performance. The two-qubit QSVM achieved the best quantum result with 72 % accuracy, whereas deeper circuits showed declining performance, indicating overfitting and reduced generalization on limited data. In contrast, the classical SVM attained 97 % accuracy with significantly lower computational effort. These findings highlight the challenges and potential of QML for cybersecurity tasks. Future work will explore circuit- expressivity tuning, optimized quantum kernels, hybrid quantum- classical approaches, and scalability to larger phishing datasets as quantum hardware evolves.
Quantum Support Vector Machines (QSVMs) combine the fundamental principles of quantum computing and classical Support Vector Machines (SVMs) to improve machine learning performance. In this paper, the author will further explore QSVM. Firstly, introduce the basics of classical SVM, including hyperplane, margin, support vector, and kernel methods. Then, introduce the basic theories of quantum computing, including quantum bits, entanglement, quantum states, superposition, and some related quantum algorithms. Focuses on the concept of QSVM, quantum kernel methods, and how SVM runs on a quantum computer. Key topics include quantum state preparation, measurement, and output interpretation. Theoretical advantages of QSVMs, such as faster computation speed, stronger performance to process high-dimensional data, and kernal computation. In addition, the author discussed the implementation of QSVM, quantum algorithms, quantum gradient descent, and optimization techniques for SVM training. The article also discusses practical issues such as error mitigation and quantum hardware requirements. The purpose of this paper is to show the advantages of QSVM by comparing SVM and QSVM.
The quantum support vector machines (QSVMs) offer a paradigm change that may leverage quantum mechanical processes to outperform traditional support vector machines (SVMs) in high-dimensional and nonlinear classification tasks. These machines are located at the crossroads of supervised machine learning and quantum computing. The purpose of this chapter is to provide a comprehensive technical analysis of QSVMs, with a particular emphasis on the use of variation quantum circuits for implicit feature space transformations and the development of these circuits within the context of quantum kernel estimation. Through the use of quantum state preparation and interference, we provide a comprehensive explanation of the possible fabrication of quantum kernels that are based on inner product evaluations in exponentially huge Hilbert spaces. When it comes to boosting model expressivity beyond classical limits, the importance that entanglement and quantum feature mapping play is specifically stressed. In addition to this, we investigate algorithmic implementations on noisy intermediate-scale quantum (NISQ) hardware, focusing on problems associated with quantum decoherence, gate fidelity, and loop depth optimization. Several fields, including quantum-enhanced drug discovery, anomaly detection in quantum sensor networks, fault classification in quantum error correction, and portfolio optimization, are now the focus of research that is being conducted in order to develop real-world applications. This chapter comes to a close with an analysis of the existing theoretical limits, resource needs, and future perspectives for the use of QSVMs in machine learning applications in order to achieve a quantum advantage. In order to facilitate the development of scalable quantum machine learning models that are founded on strong mathematical and computational notions, this synthesis is geared at academics and practitioners.
Abstract Quantum computers have the potential to speed up certain computational tasks. A possibility this opens up within the field of machine learning is the use of quantum techniques that may be inefficient to simulate classically but could provide superior performance in some tasks. Machine learning algorithms are ubiquitous in particle physics and as advances are made in quantum machine learning technology there may be a similar adoption of these quantum techniques. In this work a quantum support vector machine (QSVM) is implemented for signal-background classification. We investigate the effect of different quantum encoding circuits, the process that transforms classical data into a quantum state, on the final classification performance. We show an encoding approach that achieves an average Area Under Receiver Operating Characteristic Curve (AUC) of 0.848 determined using quantum circuit simulations. For this same dataset the best classical method tested, a classical Support Vector Machine (SVM) using the Radial Basis Function (RBF) Kernel achieved an AUC of 0.793. Using a reduced version of the dataset we then ran the algorithm on the IBM Quantum ibmq_casablanca device achieving an average AUC of 0.703. As further improvements to the error rates and availability of quantum computers materialise, they could form a new approach for data analysis in high energy physics.