Abstract Quantum machine learning is a rapidly growing field at the intersection of quantum computing and machine learning. In this work, we examine our quantum machine learning models, which are based on quantum support vector classification (QSVC) and quantum support vector regression (QSVR). We investigate these models using a quantum-circuit simulator, both with and without noise, as well as the IonQ Harmony quantum processor. For the QSVC tasks, we use a dataset containing fraudulent credit card transactions and image datasets (the MNIST and the Fashion-MNIST datasets); for the QSVR tasks, we use a financial dataset and a materials dataset. For the classification tasks, the performance of our QSVC models using 4 qubits of the trapped-ion quantum computer was comparable to that obtained from noiseless quantum-circuit simulations. The result is consistent with the analysis of our device-noise simulations with varying qubit-gate error rates. For the regression tasks, applying a low-rank approximation to the noisy quantum kernel, in combination with hyperparameter tuning in ε-SVR, improved the performance of the QSVR models on the near-term quantum device. Our results suggest that the quantum kernel, as described by our shallow quantum circuit, can be effectively used for both QSVC and QSVR tasks, indicating its resistance to noise and its adaptability to various datasets.
Abstract Quantum machine learning is a rapidly growing field at the intersection of quantum computing and machine learning. In this work, we examine our quantum machine learning models, which are based on quantum support vector classification (QSVC) and quantum support vector regression (QSVR). We investigate these models using a quantum-circuit simulator, both with and without noise, as well as the IonQ Harmony quantum processor. For the QSVC tasks, we use a dataset containing fraudulent credit card transactions and image datasets (the MNIST and the Fashion-MNIST datasets); for the QSVR tasks, we use a financial dataset and a materials dataset. For the classification tasks, the performance of our QSVC models using 4 qubits of the trapped-ion quantum computer was comparable to that obtained from noiseless quantum-circuit simulations. The result is consistent with the analysis of our device-noise simulations with varying qubit-gate error rates. For the regression tasks, applying a low-rank approximation to the noisy quantum kernel, in combination with hyperparameter tuning in ε-SVR, improved the performance of the QSVR models on the near-term quantum device. Our results suggest that the quantum kernel, as described by our shallow quantum circuit, can be effectively used for both QSVC and QSVR tasks, indicating its resistance to noise and its adaptability to various datasets.
Quantum Support Vector Regression (QSVR) has emerged as one of the most promising quantum machine learning algorithms for nonlinear regression on Noisy Intermediate-Scale Quantum (NISQ) devices. However, despite numerous simulation-based studies, experimental evaluations on physical quantum hardware remain relatively scarce. This work presents a comparative analysis of three regression approaches: classical Support Vector Regression (SVR) with a Radial Basis Function (RBF) kernel, classical SVR utilizing precomputed quantum kernels, and the native QSVR implementation available in the qiskit-machine-learning framework. Experiments were conducted on three benchmark regression datasets using three execution environments: a noiseless Qiskit Aer simulator, the IQM Adonis hardware-aware simulator, and the physical 5-qubit IQM Spark superconducting quantum computer (Odra 5) located at Wrocław University of Science and Technology. Multiple quantum feature maps and circuit depths were investigated, while model hyperparameters were optimized using grid search. The obtained results demonstrate that QSVR can be successfully executed on contemporary superconducting quantum hardware and, for selected datasets, achieves prediction accuracy comparable to or exceeding that of a classical RBF-based SVR. The experiments further reveal the significant influence of quantum hardware noise, feature map selection, and circuit depth on regression quality. Moreover, the implementation based on precomputed quantum kernels generally exhibits greater robustness on physical hardware than the native QSVR implementation. The presented benchmark provides an experimental assessment of QSVR under realistic execution conditions and contributes to the ongoing evaluation of quantum machine learning algorithms on current NISQ-era quantum computers.
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.
This study explores the performance of Quantum Support Vector Classifiers (QSVCs) and Quantum Neural Networks (QNNs) in comparison to classical models for machine learning tasks. By evaluating these models on the Iris and MNIST-PCA datasets, we find that quantum models tend to outperform classical approaches as the problem complexity increases. While QSVCs generally provide more consistent results, QNNs exhibit superior performance in higher-complexity tasks due to their increased quantum load. Additionally, we analyze the impact of hyperparameter tuning, showing that feature maps and ansatz configurations significantly influence model accuracy. We also compare the PennyLane and Qiskit frameworks, concluding that Qiskit provides better optimization and efficiency for our implementation. These findings highlight the potential of Quantum Machine Learning (QML) for complex classification problems and provide insights into model selection and optimization strategies
Quantum computing offers a powerful new paradigm for enhancing classical machine learning, particularly in classification tasks. In this paper, we examine the use of quantum kernels within Support Vector Classification (SVC) and compare their performance to classical SVC. Our experiments focus on the Iris and Wine datasets. For the Wine dataset, we applied Principal Component Analysis (PCA), reducing the feature space from 13 to 4 dimensions to improve computational efficiency. The results demonstrate that Quantum-enhanced SVC (QSVC) outperforms classical SVC, achieving an accuracy improvement from 96.15% with classical SVM to 98.05% with QSVC for the Wine dataset. Similarly, for the Iris dataset, classical SVC achieves near-perfect accuracy at 100%, while QSVC closely follows with 97.25% accuracy. These results highlight the capability of quantum kernels to improve both accuracy and efficiency in classification tasks, providing a promising direction for scalable quantum-classical hybrid systems in machine learning.
Support vector machines are powerful and frequently used machine learning methods for classification and regression tasks, which rely on the construction of kernel matrices. While crucial for the performance of this machine learning approach, choosing the most suitable kernel is highly problem-dependent. The emergence of quantum computers and quantum machine learning techniques provides new possibilities for generating powerful quantum kernels. Within this work, we solve a real-world price forecasting problem using fidelity and projected quantum kernels, which are promising candidates for the utility of near-term quantum computing. In our analysis, we examine and validate the most auspicious quantum kernels from literature and compare their performance with an optimized classical kernel. Unlike previous work on quantum support vector machines, our dataset includes categorical features that need to be encoded as numerical features, which we realize by using the one-hot-encoding scheme. One-hot-encoding, however, increases the dimensionality of the dataset significantly, which collides with the current limitations of noisy intermediate scale quantum computers. To overcome these limitations, we use autoencoders to learn a low-dimensional representation of the feature space that still maintains the most important information of the original data. To examine the impact of autoencoding, we compare the results of the encoded date with the results of the original, unencoded dataset. We could demonstrate that quantum kernels are comparable to or even better than the classical support vector machine kernels regarding the mean absolute percentage error scores for both encoded and unencoded datasets.
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.