Quantum computing is the application of Quantum mechanical resources to solve computational problems more precisely, quickly, and effectively than classical computers. Machine learning is all about discovering patterns and relationships in data. Quantum Machine Learning (QML) blends Machine Learning (ML) and Quantum Computing (QC) technologies. QML approaches may be utilized efficiently for data classification problems. Quantum Feature Maps (QFMs) are used for transferring non-linear classical data from lower input space to higher dimensional Hilbert space. Calculating the inner product between data points for classification purposes is exceedingly costly when Hilbert Space is vast. Quantum Kernel Techniques, which are immediate results of QFMs, are used to overcome this problem. In general, we cannot claim that QFMs are superior than Classical Feature Maps (CFMs); yet, there are datasets for which QFMs perform better while CFMs are less effective. It gives us the motivation behind using QFM for classification. In this paper, we proposed two new non-linear encoding functions based quantum kernels for data classification in the range [0, 2π]. The make_moons and make_circles datasets are utilized in this article to perform binary classifications using Qiskit and Sklearn. Construction of quantum kernels is performed, and Support Vector Machines (SVM) are then applied for classification. We have compared the results of our two newly proposed non-linear encoding functions to those mentioned in the literature. Our classifier's performance is approximately comparable or in some cases better to that of existing classifiers in literature.
Quantum computing is the application of Quantum mechanical resources to solve computational problems more precisely, quickly, and effectively than classical computers. Machine learning is all about discovering patterns and relationships in data. Quantum Machine Learning (QML) blends Machine Learning (ML) and Quantum Computing (QC) technologies. QML approaches may be utilized efficiently for data classification problems. Quantum Feature Maps (QFMs) are used for transferring non-linear classical data from lower input space to higher dimensional Hilbert space. Calculating the inner product between data points for classification purposes is exceedingly costly when Hilbert Space is vast. Quantum Kernel Techniques, which are immediate results of QFMs, are used to overcome this problem. In general, we cannot claim that QFMs are superior than Classical Feature Maps (CFMs); yet, there are datasets for which QFMs perform better while CFMs are less effective. It gives us the motivation behind using QFM for classification. In this paper, we proposed two new non-linear encoding functions based quantum kernels for data classification in the range [0, 2π]. The make_moons and make_circles datasets are utilized in this article to perform binary classifications using Qiskit and Sklearn. Construction of quantum kernels is performed, and Support Vector Machines (SVM) are then applied for classification. We have compared the results of our two newly proposed non-linear encoding functions to those mentioned in the literature. Our classifier's performance is approximately comparable or in some cases better to that of existing classifiers in literature.
Abstract In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of the fact that the radial basis function is recovered when data is mapped to a complex Hilbert state represented by coherent states, non-linear coherent states can be considered as a natural generalisation of the associated kernels. In this paper, as an example of kernels based on non-linear coherent states, we propose kernel functions based on generalized hypergeometric functions, as orthogonal polynomial functions. The suggested kernel is implemented with the support vector machine (SVM) on two well known datasets (make_circles, and make_moons) and outperforms the baselines, even when the level of noise is high. In addition, we study the impact of the geometrical properties of the feature space, obtained by the non-linear coherent states, on the SVM classification task, by considering the Fubini–Study metric of the associated coherent states.
Quantum machine learning has experienced significant progress in both software and hardware development in the recent years and has emerged as an applicable area of near-term quantum computers. In this work, we investigate the feasibility of utilizing quantum machine learning (QML) on real clinical datasets. We propose two QML algorithms for data classification on IBM quantum hardware: a quantum distance classifier (qDS) and a simplified quantum-kernel support vector machine (sqKSVM). We utilize these different methods using the linear time quantum data encoding technique ([Formula: see text]) for embedding classical data into quantum states and estimating the inner product on the 15-qubit IBMQ Melbourne quantum computer. We match the predictive performance of our QML approaches with prior QML methods and with their classical counterpart algorithms for three open-access clinical datasets. Our results imply that the qDS in small sample and feature count datasets outperforms kernel-based methods. In contrast, quantum kernel approaches outperform qDS in high sample and feature count datasets. We demonstrate that the [Formula: see text] encoding increases predictive performance with up to + 2% area under the receiver operator characteristics curve across all quantum machine learning approaches, thus, making it ideal for machine learning tasks executed in Noisy Intermediate Scale Quantum computers.
In this work, we studied the use of Quantum Machine Learning (QML) algorithms for binary classification and compared their performance with classical Machine Learning (ML) methods. QML merges principles of Quantum Computing (QC) and ML, offering improved efficiency and potential quantum advantage in data-driven tasks and when solving complex problems. In binary classification, where the goal is to assign data to one of two categories, QML uses quantum algorithms to process large datasets efficiently. Quantum algorithms like Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN) exploit quantum parallelism and entanglement to enhance performance over classical methods. This study focuses on two common QML algorithms, Quantum Support Vector Classifier (QSVC) and QNN. We used the Qiskit software and conducted the experiments with three different datasets. Data preprocessing included dimensionality reduction using Principal Component Analysis (PCA) and standardization using scalers. The results showed that quantum algorithms demonstrated competitive performance against their classical counterparts in terms of accuracy, while QSVC performed better than QNN. These findings suggest that QML holds potential for improving computational efficiency in binary classification tasks. This opens the way for more efficient and scalable solutions in complex classification challenges and shows the complementary role of quantum computing.
A basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely, to efficiently perform computations in an intractably large Hilbert space. In this Letter we explore some theoretical foundations of this link and show how it opens up a new avenue for the design of quantum machine learning algorithms. We interpret the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space. A quantum computer can now analyze the input data in this feature space. Based on this link, we discuss two approaches for building a quantum model for classification. In the first approach, the quantum device estimates inner products of quantum states to compute a classically intractable kernel. The kernel can be fed into any classical kernel method such as a support vector machine. In the second approach, we use a variational quantum circuit as a linear model that classifies data explicitly in Hilbert space. We illustrate these ideas with a feature map based on squeezing in a continuous-variable system, and visualize the working principle with two-dimensional minibenchmark datasets.
The classification of high-dimensional genomic data presents fundamental difficulties for classical machine learning techniques because of the intrinsic non-linearity and the enormous amount of biological feature space represented. In this report, we propose a novel Quantum Kernel Mapping Algorithm (QKMA), which utilizes quantum superposition and entanglement to place genomic data into exponentially large Hilbert spaces and discover non-linear separating hyperplanes that are not computable with classical kernel methods. Our approach to QKMA is to create a parameterized quantum circuit architecture for genomic feature encoding by utilizing principles of variational quantum eigensolvers and support vector machine optimization. We have applied QKMA to three canonical classification problems in genomics: RNA sequencing data for the classification of cancer subtypes (n = 2,847 samples), SNP-based prediction of phenotypes (n = 5,102 subjects), and classification of epigenetic methylation patterns (n = 1,634 samples). QKMA achieved classification accuracies of 91.4%, 88.7%, and 93.2%, respectively, exceeding the baseline classical RBF-SVM accuracies by 7.2%, 6.3%, and 8.1%, respectively. Furthermore, our hybrid quantum-classical optimization framework reduces the kernel computation overhead by 34% compared to naive quantum simulation methods. These results suggest that quantum kernel methods provide a principled, scalable pathway to precision genomics and have important implications for early disease detection, pharmacogenomics, and personalized medicine.
Quantum computing is a promising new approach to tackle the complex real-world computational problems by harnessing the power of quantum mechanics principles. The inherent parallelism and exponential computational power of quantum systems hold the potential to outpace classical counterparts in solving complex optimization problems, which are pervasive in machine learning. Quantum Support Vector Machine (QSVM) is a quantum machine learning algorithm inspired by classical Support Vector Machine (SVM) that exploits quantum parallelism to efficiently classify data points in high-dimensional feature spaces. We provide a comprehensive overview of the underlying principles of QSVM, elucidating how different quantum feature maps and quantum kernels enable the manipulation of quantum states to perform classification tasks. Through a comparative analysis, we reveal the quantum advantage achieved by these algorithms in terms of speedup and solution quality. As a case study, we explored the potential of quantum paradigms in the context of a real-world problem: classifying pancreatic cancer biomarker data. The Support Vector Classifier (SVC) algorithm was employed for the classical approach while the QSVM algorithm was executed on a quantum simulator provided by the Qiskit quantum computing framework. The classical approach as well as the quantum-based techniques reported similar accuracy. This uniformity suggests that these methods effectively captured similar underlying patterns in the dataset. Remarkably, quantum implementations exhibited substantially reduced execution times demonstrating the potential of quantum approaches in enhancing classification efficiency. This affirms the growing significance of quantum computing as a transformative tool for augmenting machine learning paradigms and also underscores the potency of quantum execution for computational acceleration.