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arXiv:2103.12257 · Computing and Software for Big Science

Quantum Support Vector Machines for Continuum Suppression in B Meson Decays

Jamie Heredge, Charles D. Hill, Lloyd C. L. Hollenberg, Martin E. Sevior

Published Nov 30, 2021• 6 citations
arXivHTMLPDF

Abstract

Abstract Quantum computers have the potential to speed up certain computational tasks. A possibility this opens up within the field of machine learning is the use of quantum techniques that may be inefficient to simulate classically but could provide superior performance in some tasks. Machine learning algorithms are ubiquitous in particle physics and as advances are made in quantum machine learning technology there may be a similar adoption of these quantum techniques. In this work a quantum support vector machine (QSVM) is implemented for signal-background classification. We investigate the effect of different quantum encoding circuits, the process that transforms classical data into a quantum state, on the final classification performance. We show an encoding approach that achieves an average Area Under Receiver Operating Characteristic Curve (AUC) of 0.848 determined using quantum circuit simulations. For this same dataset the best classical method tested, a classical Support Vector Machine (SVM) using the Radial Basis Function (RBF) Kernel achieved an AUC of 0.793. Using a reduced version of the dataset we then ran the algorithm on the IBM Quantum ibmq_casablanca device achieving an average AUC of 0.703. As further improvements to the error rates and availability of quantum computers materialise, they could form a new approach for data analysis in high energy physics.

DOI
10.1007/s41781-021-00075-x

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Quantum machine learning is at the crossroads of two of the most exciting current areas of research; quantum computing and classical machine learning. It explores the interaction between quantum computing and machine learning, investigating how results and techniques from one field can be used to solve the problems of the other. Here, we investigate quantum support vector machine (QSVM) algorithm and its circuit version on present quantum computers. We propose a general encoding procedure extending QSVM algorithm, which would allow one to feed vectors with higher dimension in the training-data oracle of QSVM. We compute the efficiency of the QSVM circuit implementation method by encoding training and testing data sample in quantum circuits and running them on quantum simulator and real chip for two datasets; 6/9 and banknote. We highlight the technical difficulties one would face while applying the QSVM algorithm on current NISQ era devices. Then we propose a new method to classify these datasets with enhanced efficiencies for the above datasets both on simulator and real chips.
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The evolution of quantum computers and quantum machine learning (QML) algorithms have started demonstrating exponential speed-ups. In machine learning problems, the efficient handling and manipulation of linear algebra subroutines defines the complexity of the task to be performed. Quantum computers handle big datasets in the form of vectors and matrix operations very efficiently. In this paper, quantum support vector machine (QSVM) algorithm is used to solve a classification problem using a benchmarking MNIST dataset of handwritten images of digits. Quantum SVM variational and kernel matrix algorithms are implemented to analyze quantum speedup on quantum simulator and physical quantum processor back-ends. The study compared classical and quantum SVM algorithms in terms of execution time and accuracy. The results explicitly prove quantum speed-up achieved by quantum classifiers on quantum back-ends for machine learning applications.
Abstract Quantum computing has demonstrated a potential advantage in advancing artificial intelligence and machine learning applications. Both disciplines leverage higher-dimensional computation that relies on complex linear algebra operations. Quantum Support Vector Machines (QSVMs) uses quantum computation principles to enhance classification performance over traditional SVMs. This paper studies QSVMs applied to the Iris and Wine datasets by exploring various quantum encoding methods, including amplitude encoding, ZZFeatureMap, and PauliFeatureMap, within IBM’s Qiskit framework. These encoding methods enable QSVMs to utilize quantum phenomena like superposition and entanglement to transform classical data into quantum states to increase computational efficiency and accuracy in classification tasks. Numerical results indicate that QSVMs with amplitude encoding with combination of ZZFeatureMap achieve higher classification accuracy than traditional techniques. Also, this study assess the current performance of Noisy Intermediate-Scale Quantum (NISQ) devices to highlight the need for further optimization and advancements in quantum data encoding approches. These findings provide important insights into the application of QSVMs and their potential to address a range of classification problems effectively.
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.