Abstract Quantum machine learning (QML) is anticipated to exhibit enhanced computing abilities as compared to its classical counterpart. However, one of the key issues in its potentially superior performance is the creation and propagation of quantum errors in quantum circuits. In Noisy Intermediate Scale Quantum (NISQ) era, one of the remedies is to impose the constraints on the number of quantum resources and to restrict the depth of quantum circuits. However, in the case of very large number of features in the data-sets, QML with restricted quantum resources may not yield reliable classification accuracy. In order to address these limitations, this study introduces a novel approach that leverages QML through precision matrix-based feature selection. More specifically, we considered the quantum version of support vector machines (PM-QSVM) to analyze the impact of the suggested feature selection mechanism. In addition, the impact of various kernel based quantum encodings of the selected features is also investigated. Moreover, the sensitivity analysis is carried out to ascertain the reliability of the feature selection mechanism. Our findings and the experimental results demonstrate how the integration of the suggested mechanism with quantum computing can enhance the decision making process.
Abstract Quantum machine learning (QML) is anticipated to exhibit enhanced computing abilities as compared to its classical counterpart. However, one of the key issues in its potentially superior performance is the creation and propagation of quantum errors in quantum circuits. In Noisy Intermediate Scale Quantum (NISQ) era, one of the remedies is to impose the constraints on the number of quantum resources and to restrict the depth of quantum circuits. However, in the case of very large number of features in the data-sets, QML with restricted quantum resources may not yield reliable classification accuracy. In order to address these limitations, this study introduces a novel approach that leverages QML through precision matrix-based feature selection. More specifically, we considered the quantum version of support vector machines (PM-QSVM) to analyze the impact of the suggested feature selection mechanism. In addition, the impact of various kernel based quantum encodings of the selected features is also investigated. Moreover, the sensitivity analysis is carried out to ascertain the reliability of the feature selection mechanism. Our findings and the experimental results demonstrate how the integration of the suggested mechanism with quantum computing can enhance the decision making process.
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 combines the power of quantum computing with machine learning to address complex computational challenges. In this work, we propose an integrated approach that leverages Quantum Non-Negative Matrix Factorization (QNMF) for feature selection and dimensionality reduction, coupled with Quantum Support Vector Machines (QSVM) for accurate classification. By combining the strengths of these two quantum techniques, our approach reduces data complexity while maintaining classification accuracy. We evaluate the performance of our method across multiple datasets from finance, healthcare, and e-commerce. Experimental results demonstrate that the proposed QNMF+QSVM approach achieves superior accuracy compared to classical machine learning methods such as SVM, Random Forests, and Decision Trees, highlighting its potential for solving real-world classification problems.
In order to leverage quantum computers for machine learning tasks such as image classification, careful consideration is required: NISQ-era quantum computers have limitations, which include noise, scalability, read-in and read-out times, and gate operation times. Therefore, strategies should be devised to mitigate the impact that complex datasets can have on the overall efficiency of a quantum machine learning pipeline. This may otherwise lead to excessive resource demands or increased noise. We apply a classical feature extraction method using a ResNet10-inspired convolutional autoencoder to both reduce the dimensionality of the dataset and extract abstract and meaningful features before feeding them into a quantum machine learning block. The quantum block of choice is a quantum-enhanced support vector machine (QSVM), as support vector machines 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. Three image datasets are used to illustrate the pipeline: HTRU-1, MNIST, and CIFAR-10. We also include a quantum-enhanced one-class support vector machine (QOCSVM) for the highly unbalanced HTRU-1 set, as well as classical machine learning results to serve as a benchmark. Finally, the HTRU-2 dataset is also included to serve as a benchmark for a dataset with well-correlated features. The autoencoder achieved near-perfect reconstruction and high classification accuracy for MNIST, while CIFAR-10 showed poorer performance due to image complexity, and HTRU-1 struggled because of dataset imbalance. This highlights the need for a balance between dimensionality reduction through classical feature extraction and prediction performance using quantum methods.
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.
The rapid advancement of quantum computing hardware and software has ushered in a new era for computational science, promising to tackle problems that are intractable for classical computers. Parallelly, machine learning (ML) has revolutionized data analysis and artificial intelligence. The confluence of these two fields, known as Quantum Machine Learning (QML), aims to harness the principles of quantum mechanics-such as superposition, entanglement, and interference-to enhance and redefine classical machine learning algorithms. This survey provides a comprehensive overview of the burgeoning field of QML. We begin by elucidating the fundamental quantum concepts that underpin QML approaches. We then present a detailed taxonomy and analysis of prominent QML algorithms, categorizing them into quantum-enhanced classical models and fully quantum models. Key families of algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Neural Networks (QNNs), and Quantum Generative Adversarial Networks (QGANs). For each, we explain the theoretical quantum advantage, the circuit implementation, and the current limitations. Furthermore, we delve into the critical challenges facing the practical realization of QML, including the pervasive issue of noise in Noisy Intermediate-Scale Quantum (NISQ) devices, the problem of barren plateaus in training quantum circuits, and the complexities of efficient data encoding (quantum feature maps). We also present a small-scale experimental simulation of a variational quantum classifier on a standardized dataset, demonstrating its principle and comparing its performance with a classical counterpart. Finally, the paper discusses the future trajectory of QML, highlighting the importance of error mitigation, hybrid quantum-classical architectures, and the development of quantum-specific learning inductive biases. We conclude that while fault-tolerant quantum computers remain on the horizon, QML represents a paradigm shift with the potential to deliver profound computational advantages in the coming decades.
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.