Quantum Support Vector Classifiers have been gaining traction in solving classification problems as it enables efficient kernel estimation and potential improvement in accuracy. To estimate the kernel matrices, a quantum kernel needs a Pauli Feature Map which encodes the classical data into the quantum state space. For a given dataset and dimension, we can have an exorbitant number of Pauli Feature Maps. Hence, finding a Pauli Feature Map that maximizes model accuracy is a research challenge. To address this optimization problem, we propose an algorithm that finds a near-optimal Pauli Feature Map by solving several sub-problems with varying numbers of decision variables and their constraints. Each sub-problem aims to find the Pauli Feature Map that maximizes the model accuracy. We use genetic algorithm to solve each sub-problem, and then select the best out of all the near-optimal Pauli Feature Maps. Instead of formulating a single optimization problem, we use this divide-and-conquer approach (of breaking down the problem into multiple sub-problems) to reduce the overall search space. To evaluate the efficiency of our algorithm, we compare it against solving each sub-problem through exhaustive approach. The latter yields the optimal Pauli Feature Map by exploring the full state space. For the scikit-learn Breast Cancer dataset with dimension 5, our algorithm converges to the optimal Pauli Feature Map in about 804 seconds which is over 4 times faster than the exhaustive approach.
Quantum Support Vector Classifiers have been gaining traction in solving classification problems as it enables efficient kernel estimation and potential improvement in accuracy. To estimate the kernel matrices, a quantum kernel needs a Pauli Feature Map which encodes the classical data into the quantum state space. For a given dataset and dimension, we can have an exorbitant number of Pauli Feature Maps. Hence, finding a Pauli Feature Map that maximizes model accuracy is a research challenge. To address this optimization problem, we propose an algorithm that finds a near-optimal Pauli Feature Map by solving several sub-problems with varying numbers of decision variables and their constraints. Each sub-problem aims to find the Pauli Feature Map that maximizes the model accuracy. We use genetic algorithm to solve each sub-problem, and then select the best out of all the near-optimal Pauli Feature Maps. Instead of formulating a single optimization problem, we use this divide-and-conquer approach (of breaking down the problem into multiple sub-problems) to reduce the overall search space. To evaluate the efficiency of our algorithm, we compare it against solving each sub-problem through exhaustive approach. The latter yields the optimal Pauli Feature Map by exploring the full state space. For the scikit-learn Breast Cancer dataset with dimension 5, our algorithm converges to the optimal Pauli Feature Map in about 804 seconds which is over 4 times faster than the exhaustive approach.
Background: Classical algorithms often struggle with the high dimensionality of medical data critical for early lung cancer diagnosis. While Quantum Machine Learning (QML) offers enhanced pattern recognition capabilities, the impact of specific quantum feature encoding strategies on diagnostic accuracy remains underexplored.Methods: We evaluated Quantum Support Vector Machines (QSVM) using a dataset of 309 lung cancer patients, divided into six balanced subsets to mitigate class imbalance. Models were implemented on a qasm simulator, comparing three encoding strategies: ZFeatureMap, ZZFeatureMap, and PauliFeatureMap. Performance was assessed using standard classification metrics.Results: The choice of feature map significantly influenced model efficacy. The PauliFeatureMap outperformed other kernels, achieving 100% classification accuracy in three of the six subsets, whereas ZFeatureMap and ZZFeatureMap yielded lower predictive consistency.Conclusion: Quantum feature map selection is a decisive factor in QSVM performance. Specifically, the PauliFeatureMap demonstrates high separability for medical data, highlighting the potential of optimized quantum kernels to improve diagnostic precision.
Abstract Feature selection is critical in machine learning to reduce dimensionality and improve model accuracy and efficiency. The exponential growth in feature space dimensionality for modern datasets directly results in ambiguous samples and redundant features, which can severely degrade classification accuracy. Quantum machine learning offers potential advantages for addressing this challenge. In this paper, we propose a novel method, quantum support vector machine feature selection (QSVMF), integrating quantum support vector machines with multi-objective genetic algorithm. QSVMF optimizes multiple simultaneous objectives: maximizing classification accuracy, minimizing selected features and quantum circuit costs, and reducing feature covariance. We apply QSVMF for feature selection on a breast cancer dataset, comparing the performance of QSVMF against classical approaches with the selected features. Experimental results show that QSVMF achieves superior performance. Furthermore, the Pareto front solutions of QSVMF enable analysis of accuracy versus feature set size trade-offs, identifying extremely sparse yet accurate feature subsets. We contextualize the biological relevance of the selected features in terms of known breast cancer biomarkers. This work highlights the potential of quantum-based feature selection to enhance machine learning efficiency and performance on complex real-world data.
The minimum accuracy heuristic evaluates quantum feature maps without requiring full quantum support vector machine (QSVM) training. However, the original formulation is computationally expensive, restricted to balanced datasets, and lacks theoretical backing. This work generalizes the metric to arbitrary binary datasets and formally proves it constitutes a certified lower bound on the optimal empirical accuracy of any linear classifier in the same feature space. Furthermore, we introduce Monte Carlo strategies to efficiently estimate this bound using a random subset of Pauli directions, accompanied by rigorous probabilistic guarantees. These contributions establish minimum accuracy as a scalable, theoretically sound tool for pre-screening feature maps on near-term quantum devices.
Quantum Support Vector Machines (QSVM) is one of the most promising frameworks in quantum machine learning, yet their performance depends on the design of the feature map. Conventional approaches rely on fixed quantum circuits, which often fail to generalize across datasets. To address this limitation, we propose GA-QSVM, a hybrid framework that employs Genetic Algorithms (GA) to automatically optimize feature maps. The proposed method introduces a configurable framework that flexibly defines the evolutionary parameters, enabling the construction of adaptive circuits. Experimental evaluation of datasets, including Digits, Fashion, Wine, and Breast Cancer, demonstrates that GA-QSVMs achieve a comparable accuracy compared to classical SVMs and standard QSVMs. Furthermore, transfer learning results indicate that GA-QSVM's circuits generalize effectively across datasets. These findings highlight the potential of evolutionary strategies to automate and enhance kernel design for future quantum machine learning applications.
The support vector machine algorithm with a quantum kernel estimator (QSVM-Kernel), as a leading example of a quantum machine learning technique, has undergone significant advancements. Nevertheless, its integration with classical data presents unique challenges. While quantum computers primarily interact with data in quantum states, embedding classical data into quantum states using feature mapping techniques is essential for leveraging quantum algorithms Despite the recognized importance of feature mapping, its specific impact on data classification outcomes remains largely unexplored. This study addresses this gap by comprehensively assessing the effects of various feature mapping methods on classification results, taking medical data analysis as a case study. In this study, the QSVM-Kernel method was applied to classification problems in two different and publicly available medical datasets, namely, the Wisconsin Breast Cancer (original) and The Cancer Genome Atlas (TCGA) Glioma datasets. In the QSVM-Kernel algorithm, quantum kernel matrices obtained from 9 different quantum feature maps were used. Thus, the effects of these quantum feature maps on the classification results of the QSVM-Kernel algorithm were examined in terms of both classifier performance and total execution time. As a result, in the Wisconsin Breast Cancer (original) and TCGA Glioma datasets, when Rx and Ry rotational gates were used, respectively, as feature maps in the QSVM-Kernel algorithm, the best classification performances were achieved both in terms of classification performance and total execution time. The contributions of this study are that (1) it highlights the significant impact of feature mapping techniques on medical data classification outcomes using the QSVM-Kernel algorithm, and (2) it also guides undertaking research for improved QSVM classification performance.
In this study, the performance of classical and quantum machine learning models was compared using the Breast Cancer dataset, which consists of diagnostic data aimed at classifying breast tumor types. Breast cancer, being one of the most common and life-threatening cancers in women, requires accurate diagnostic tools for early detection and effective treatment. The primary objective of this study is to evaluate the accuracy of quantum-assisted models through quantum feature selection methods. Initially, classical machine learning algorithms such as Support Vector Machines (SVM), Decision Trees, Random Forests, and Logistic Regression were applied to the dataset for baseline analysis. Subsequently, a quantum feature map was constructed using the Cirq library, enabling feature transformation based on this map. The classification was performed using the SVM model with the quantum-transformed features. The Logistic Regression and SVM models demonstrated the highest performance among classical machine learning models, achieving an accuracy rate of 96.49%, followed by Random Forest at 94.74% and Decision Tree at 92.11%. In the context of quantum feature transformation, the model utilizing the top five selected features achieved an accuracy rate of 94.74%, in contrast to 98.25% for the model trained with all features. These findings underscore the potential of quantum feature maps in enhancing model performance compared to classical techniques. The results suggest that quantum computing may offer significant advantages when integrated into machine learning frameworks, particularly in domains such as medical diagnostics, where high accuracy is crucial.