Quantum Support Vector Machine Research Articles

Quantum support vector machines: theory and applications

Abstract. 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.

Enhanced QSVM with elitist non‐dominated sorting genetic optimisation algorithm for breast cancer diagnosis

AbstractMachine learning has emerged as a promising method for predicting breast cancer using quantum computation techniques. Quantum machine learning algorithms, such as quantum support vector machines (QSVMs), are demonstrating superior efficiency and economy in tackling complex problems compared to traditional machine learning methods. When compared with classical support vector machine, the quantum machine produces remarkably accurate results. The suggested quantum SVM model in this study effectively resolved the binary classification problem for diagnosing malignant breast cancer. This work introduces an enhanced approach to breast cancer diagnosis by integrating QSVM with elitist non‐dominated sorting genetic optimization (ENSGA), leveraging the strengths of both techniques to achieve more accurate and efficient classification results. ENSGA plays a crucial role in optimising QSVM parameters, ensuring that the model attains the best possible classification accuracy while considering multiple objectives simultaneously. Moreover, the quantum kernel estimation method demonstrated exceptional performance by achieving high accuracy within an impressive execution time of 0.14 in the IBM QSVM simulator. The seamless integration of quantum computation techniques with optimisation strategies such as ENSGA highlights the potential of quantum machine learning in revolutionising the field of healthcare, particularly in the domain of breast cancer diagnosis.

An advanced quantum support vector machine for power quality disturbance detection and identification

Quantum algorithms have demonstrated extraordinary potential across numerous fields, offering significant advantages in solving practical problems. Power Quality Disturbances (PQDs) have always been a critical factor affecting the stability and safety of electrical power systems, and accurately detecting and identifying PQDs is crucial for ensuring reliable system operation. This paper explores the application of quantum algorithms in the field of power quality and proposes a novel method using Quantum Support Vector Machines (QSVM) to detect and identify PQDs, which marks the first application of QSVM in PQD analysis. The QSVM model employed involves three main stages: quantum feature mapping, quantum kernel computation, and model training. Quantum feature mapping uses quantum circuits to map classical data into a high-dimensional Hilbert space, enhancing feature separability. Quantum kernel computation calculates the inner products between features for model training. Rigorous theoretical and experimental analyses validate our approach. This method achieves a time complexity of O(N2log(N))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$O(N^{2} \\log (N))$\\end{document}, superior to classical SVM algorithms. Simulation results show high accuracy in PQDs detection, achieving a 100% detection rate and a 96.25% accuracy rate in single PQD identification. Experimental outcomes demonstrate robustness, maintaining over 87% accuracy even with increased noise levels, confirming its effectiveness in PQDs detection and identification.

Quantum machine learning for additive manufacturing process monitoring

Machine learning is useful for analyzing and monitoring complex manufacturing processes. However, it has several limitations including the curse-of-dimensionality and lack of training data. In this paper, we propose a quantum machine learning strategy to tackle these challenges. Quantum support vector machine is applied to identify the states of machines in fused filament fabrication process based on acoustic emission data. Quantum convolutional neural network is used to detect spatters in laser powder bed fusion process based on coaxial optical images. Our results show that quantum machine learning can achieve the similar accuracy levels of predictions by classical machine learning counterparts, but with exponentially fewer parameters.

Quantum Machine Learning: Bridging Quantum Computing and Artificial Intelligence

Abstract: This comprehensive article explores the burgeoning field of Quantum Machine Learning (QML), examining its foundational principles, key algorithms, and potential applications. We delve into the fundamentals of quantum computing, including qubits, quantum gates, and the challenges of quantum measurement and decoherence. The article provides an indepth analysis of Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN), comparing them with their classical counterparts and highlighting their unique advantages and limitations. We investigate the promising applications of QML in material science, cryptography, and optimization problems, showcasing its potential to revolutionize drug discovery, secure communication, and complex problem-solving. The review also addresses the significant challenges facing QML, including hardware constraints, error correction, algorithm development, and integration with classical systems. By synthesizing current research and identifying future directions, this article offers a comprehensive overview of QML's transformative potential in artificial intelligence and computational science, while acknowledging the hurdles that must be overcome to fully realize its capabilities.

Quantum Machine Learning: Leveraging Quantum Computing for Enhanced Learning Algorithms

The paper "Quantum Machine Learning: Leveraging Quantum Computing for Enhanced Learning Algorithms" explores the integration of quantum computing principles into classical machine learning techniques, aiming to address limitations such as scalability and computational inefficiency. It presents the foundational concepts of quantum computing, including superposition and entanglement, and their application in accelerating machine learning processes. The study emphasizes the potential for quantum algorithms to significantly improve the performance of machine learning tasks by processing large datasets more efficiently and exploring larger hypothesis spaces. Key quantum machine learning algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Principal Component Analysis (QPCA), and Quantum Neural Networks (QNN), each of which leverages quantum mechanics to overcome the computational barriers faced by classical algorithms. The Quantum Approximate Optimization Algorithm (QAOA) is also highlighted for its ability to optimize machine learning models more effectively. While the theoretical benefits of Quantum Machine Learning (QML) are promising, the practical application of these techniques is currently limited by the constraints of existing quantum hardware. This research contributes to the emerging field of QML by examining its potential advantages and future implications in addressing complex data processing challenges.

The Effect of Linear Discriminant Analysis and Quantum Feature Maps on QSVM Performance for Obesity Diagnosis

Obesity, characterized by an excessive increase in body fat, is not only a significant disease but also a condition that serves as the basis for many other illnesses. Therefore, early intervention and necessary precautions for diagnosing and treating obesity are of paramount importance. Classical machine learning algorithms are actively utilized in medical fields to expedite prediction processes. However, the increasing volume of data renders even effective classification algorithms inadequate for experts to diagnose diseases. Quantum computing-based algorithms come into play at this point, offering a new perspective in machine learning by utilizing quantum physics, which is contrary to the rules of classical physics. Dimensionality reduction techniques required for the use of quantum-based algorithms play an essential role in both classical and quantum applications. In this study, Linear Discriminant Analysis (LDA) and Principal Component Analysis (PCA), classical dimensionality reduction methods, were applied to the obesity dataset and analyzed with Quantum Support Vector Machine (QSVM) and Support Vector Machine (SVM) algorithms. To conduct QSVM studies, the comparison of three different quantum feature maps providing the qubit transformation of classical bit data is also included in this study. As a result of the analysis, it was determined that the proposed method as LDA-QSVM achieved 100% success when used with Z and Pauli X feature maps. This success, which is rare in literature studies on obesity data, emphasizes the future potential of quantum-based algorithms in obesity diagnosis and treatment.

Pulsar classification: comparing quantum convolutional neural networks and quantum support vector machines

Well-known quantum machine learning techniques, specifically quantum kernel-assisted support vector machines (QSVMs) and quantum convolutional neural networks (QCNNs), are applied to the binary classification of pulsars. In this comparative study, it is illustrated with simulations that both quantum methods successfully achieve effective classification of the HTRU-2 data set that connects pulsar class labels to eight separate features. While QCNNs are superior in terms of training and prediction speed compared to QSVMs, the preference shifts toward QSVMs when the present noisy NISQ-era devices are incorporated into the comparison. QSVMs demonstrate superior overall performance compared to QCNNs when assessed using binary classification performance metrics. Classical methods are implemented to serve as a benchmark for comparison with the quantum approaches.

RA-XTNet: A Novel CNN Model to Predict Rheumatoid Arthritis from Hand Radiographs and Thermal Images: A Comparison with CNN Transformer and Quantum Computing.

The aim and objective of the research are to develop an automated diagnosis system for the prediction of rheumatoid arthritis (RA) based on artificial intelligence (AI) and quantum computing for hand radiographs and thermal images. The hand radiographs and thermal images were segmented using a UNet++ model and color-based k-means clustering technique, respectively. The attributes from the segmented regions were generated using the Speeded-Up Robust Features (SURF) feature extractor and classification was performed using k-star and Hoeffding classifiers. For the ground truth and the predicted test image, the study utilizing UNet++ segmentation achieved a pixel-wise accuracy of 98.75%, an intersection over union (IoU) of 0.87, and a dice coefficient of 0.86, indicating a high level of similarity. The custom RA-X-ray thermal imaging (XTNet) surpassed all the models for the detection of RA with a classification accuracy of 90% and 93% for X-ray and thermal imaging modalities, respectively. Furthermore, the study employed quantum support vector machine (QSVM) as a quantum computing approach which yielded an accuracy of 93.75% and 87.5% for the detection of RA from hand X-ray and thermal images. In addition, vision transformer (ViT) was employed to classify RA which obtained an accuracy of 80% for hand X-rays and 90% for thermal images. Thus, depending on the performance measures, the RA-XTNet model can be used as an effective automated diagnostic method to diagnose RA accurately and rapidly in hand radiographs and thermal images.

An enhanced approach for predicting air pollution using quantum support vector machine

The essence of quantum machine learning is to optimize problem-solving by executing machine learning algorithms on quantum computers and exploiting potent laws such as superposition and entanglement. Support vector machine (SVM) is widely recognized as one of the most effective classification machine learning techniques currently available. Since, in conventional systems, the SVM kernel technique tends to sluggish down and even fail as datasets become increasingly complex or jumbled. To compare the execution time and accuracy of conventional SVM classification to that of quantum SVM classification, the appropriate quantum features for mapping need to be selected. As the dataset grows complex, the importance of selecting an appropriate feature map that outperforms or performs as well as the classification grows. This paper utilizes conventional SVM to select an optimal feature map and benchmark dataset for predicting air quality. Experimental evidence demonstrates that the precision of quantum SVM surpasses that of classical SVM for air quality assessment. Using quantum labs from IBM’s quantum computer cloud, conventional and quantum computing have been compared. When applied to the same dataset, the conventional SVM achieved an accuracy of 91% and 87% respectively, whereas the quantum SVM demonstrated an accuracy of 97% and 94% respectively for air quality prediction. The study introduces the use of quantum Support Vector Machines (SVM) for predicting air quality. It emphasizes the novel method of choosing the best quantum feature maps. Through the utilization of quantum-enhanced feature mapping, our objective is to exceed the constraints of classical SVM and achieve unparalleled levels of precision and effectiveness. We conduct precise experiments utilizing IBM’s state-of-the-art quantum computer cloud to compare the performance of conventional and quantum SVM algorithms on a shared dataset.

Optimize the event selection strategy to study the anomalous quartic gauge couplings at muon colliders using the support vector machine and quantum support vector machine

The search of the new physics (NP) beyond the Standard Model is one of the most important topics in current high energy physics. With the increasing luminosities at the colliders, the search for NP signals requires the analysis of more and more data, and the efficiency in data processing becomes particularly important. As a machine learning algorithm, support vector machine (SVM) is expected to to be useful in the search of NP. Meanwhile, the quantum computing has the potential to offer huge advantages when dealing with large amounts of data, which suggests that quantum SVM (QSVM) is a potential tool in future phenomenological studies of the NP. How to use SVM and QSVM to optimize event selection strategies to search for NP signals are studied in this paper. Taking the tri-photon process at a muon collider as an example, it can be shown that the event selection strategies optimized by the SVM and QSVM are effective in the search of the dimension-8 operators contributing to the anomalous quartic gauge couplings.

Developing intelligent cyber threat detection systems through quantum computing

In the face of increasingly sophisticated cyber threats, traditional detection systems often fall short in protecting critical supply chains. This research presents the development and evaluation of an intelligent cyber threat detection system integrating Quantum Computing (QC) and Artificial Intelligence (AI). The proposed system significantly enhances detection accuracy, reduces latency, and improves resource efficiency compared to traditional methods. Quantum algorithms, such as Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN), demonstrated superior performance with accuracies of 95.2% and 96.7%, respectively. The system achieved high detection rates for various cyber threats, including malware, phishing, ransomware, and advanced persistent threats (APTs), with reduced false positive rates. The integration of QC also resulted in faster threat detection and response times, with system latency halved across key components. These advancements provide substantial benefits for cyber threat response in supply chains, ensuring robust protection of financial transactions and critical infrastructure. The enhanced scalability and efficiency make the system a valuable asset for safeguarding the United States' financial sector against sophisticated cyber-attacks.

Implementation of quantum machine learning in predicting corrosion inhibition efficiency of expired drugs

This study explores the potential of quantum machine learning (QML) 's potential in predicting expired pharmaceutical compounds' corrosion inhibition capacity. This investigation utilized a QSPR model where features derived from density functional theory (DFT) calculations are used as input, while the corrosion inhibition efficiency (CIE) values derived from the experimental study are used as target output. The proposed QML model exhibits varying performance through evaluation metrics, particularly concerning encoding and ansatz design. Notably, the quantum support vector machine (QSVM) demonstrates superior predictive performance compared to the variational quantum circuit (VQC) and quantum neural network (QNN). Specifically, the QSVM model achieves the highest scores in evaluation metrics, with a root mean squared error (RMSE) of 4.36, mean absolute error (MAE) of 3.19, and mean absolute deviation (MAD) of 3.08. The research highlights the importance of larger datasets to improve predictability and emphasizes the potential of QML in investigating anti-corrosion materials. Despite its limitations, this study establishes a foundational framework for utilizing QML to forecast anti-corrosive qualities.

Quantum Support Vector Machine for Classification Task: A Review

Quantum computing has emerged as a promising technology capable of solving complex computational problems more efficiently than classical computers. Among the various quantum algorithms developed, the Quantum Support Vector Machine (QSVM) has gained significant attention for its potential to enhance machine learning tasks, particularly classification. This review paper explores the theoretical foundations, methodologies, and potential advantages of QSVM for classification tasks. We discuss the quantum computing principles underpinning QSVM, compare them with classical support vector machines, and review recent advancements and applications. Finally, we highlight the challenges and prospects of QSVM in the context of quantum machine learning.

Quantum support vector machine for multi classification

Classical machine learning algorithms seem to be totally incapable of processing tremendous data, while quantum machine learning algorithms could deal with big data unhurriedly and provide exponential acceleration over classical counterparts. In this paper, we propose two quantum support vector machine algorithms for multi classification. One is the quantum version of the directed acyclic graph support vector machine. The other one is to use the Grover search algorithm before measurement, which amplifies the amplitude of the phase storing of the classification result. For k classification, the former provides quadratic reduction in computational complexity when classifying. The latter accelerates the training speed significantly and more importantly, the classification result can be read out with a probability of at least 50% using only one measurement. We conduct numerical simulations on two algorithms, and their classification success rates are 96% and 88.7%, respectively.

Quantum kernels for classifying dynamical singularities in a multiqubit system

Dynamical quantum phase transition is a critical phenomenon involving out-of-equilibrium states and broken symmetries without classical analogy. However, when finite-sized systems are analyzed, dynamical singularities of the rate function can appear, leading to a challenging physical characterization when parameters are changed. Here, we report a quantum support vector machine algorithm that uses quantum Kernels to classify dynamical singularities of the rate function for a multiqubit system. We illustrate our approach using N long-range interacting qubits subjected to an arbitrary magnetic field, which induces a quench dynamics. Inspired by physical arguments, we introduce two different quantum Kernels, one inspired by the ground state manifold and the other based on a single state tomography. Our accuracy and adaptability results show that this quantum dynamical critical problem can be efficiently solved using physically inspiring quantum Kernels. Moreover, we extend our results for the case of time-dependent fields, quantum master equation, and when we increase the number of qubits.

Evaluation of conventional and quantum computing for predicting mortality based on small early-onset colorectal cancer data

BackgroundQuantum computing integrated with machine learning (ML) offers novel solutions in various fields, including healthcare. The synergy between quantum computing and ML in classification exploits unique data patterns. Despite theoretical advantages, the empirical application and effectiveness of quantum computing on small medical datasets remains underexplored. MethodThis retrospective study from a tertiary hospital used data on early-onset colorectal cancer with 93 features and 1501 patients from 2008 to 2020 to predict mortality. We compared quantum support vector machine (QSVM) models with classical SVM models in terms of number of features, number of training sets, and outcome ratio. We evaluated the model based on the area under the curve in the receiver operating characteristic curve (AUROC). ResultsWe observed a mortality rate of 7.6 % (96 of 1253 subjects). We generated the mortality prediction model using 11 clinical variables, including cancer stage and chemotherapy history. We found that the AUROC difference between the conventional and quantum methods was the maximum for the top 11 variables. We also showed the AUROC in QSVM (mean [standard deviation], 0.863 [0.102]) outperformed all the number of trials in the conventional SVM (0.723 [0.231]). Compared to the conventional SVM, the QSVM showed robust performance, consistent with the AUROC, even in the unbalanced case. ConclusionOur study highlights the potential of quantum computing to improve predictive modeling in healthcare, especially for rare diseases with limited available data. The advantages of quantum computing, such as the exploration of Hilbert space, contributed to the superior predictive performance compared to conventional methods.

Solving the vehicle routing problem via quantum support vector machines

The vehicle routing problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most efficient and economical manner possible. Quantum machine learning offers a new way to obtain solutions by harnessing the natural speedups of quantum effects, although many solutions and methodologies are modified using classical tools to provide excellent approximations of the VRP. In this paper, we employ 6 and 12 qubit circuits, respectively, to build and evaluate a hybrid quantum machine learning approach for solving VRP of 3- and 4-city scenarios. The approach employs quantum support vector machines (QSVMs) trained using a variational quantum eigensolver on a static or dynamic ansatz. Different encoding strategies are used in the experiment to transform the VRP formulation into a QSVM and solve it. Multiple optimizers from the IBM Qiskit framework are also evaluated and compared

Quantum support vector machine for forecasting house energy consumption: a comparative study with deep learning models

The Smart Grid operates autonomously, facilitating the smooth integration of diverse power generation sources into the grid, thereby ensuring a continuous, reliable, and high-quality supply of electricity to end users. One key focus within the realm of smart grid applications is the Home Energy Management System (HEMS), which holds significant importance given the fluctuating availability of generation and the dynamic nature of loading conditions. This paper presents an overview of HEMS and the methodologies utilized for load forecasting. It introduces a novel approach employing Quantum Support Vector Machine (QSVM) for predicting periodic power consumption, leveraging the AMPD2 dataset. In the establishment of a microgrid, various factors such as energy consumption patterns of household appliances, solar irradiance, and overall load are taken into account in dataset creation. In the realm of load forecasting in Home Energy Management Systems (HEMS), the Quantum Support Vector Machine (QSVM) stands out from other methods due to its unique approach and capabilities. Unlike traditional forecasting methods, QSVM leverages quantum computing principles to handle complex and nonlinear electricity consumption patterns. QSVM demonstrates superior accuracy by effectively capturing intricate relationships within the data, leading to more precise predictions. Its ability to adapt to diverse datasets and produce significantly low error values, such as RMSE and MAE, showcases its efficiency in forecasting electricity load consumption in smart grids. Moreover, the QSVM model’s exceptional flexibility and performance, as evidenced by achieving an accuracy of 97.3% on challenging datasets like AMpds2, highlight its distinctive edge over conventional forecasting techniques, making it a promising solution for enhancing forecasting accuracy in HEMS.The article provides a brief summary of HEMS and load forecasting techniques, demonstrating and comparing them with deep learning models to showcase the efficacy of the proposed algorithms.

Quantum support vector machines for classification and regression on a trapped-ion quantum computer

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. The alignment, as measured by the Frobenius inner product between the noiseless and noisy quantum kernels, can serve as an indicator of the relative prediction performance on noisy quantum devices in comparison with their ideal counterparts. 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.