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IEEE Transactions on Computers

Quantum Support Vector Machine for Classifying Noisy Data

Jiaye Li, Yangding Li, Jiagang Song, Jian Zhang, Shichao Zhang

Published Jun 19, 2024• 61 citations
Publisher

Abstract

Noisy data is ubiquitous in quantum computer, greatly affecting the performance of various algorithms. However, existing quantum support vector machine models are not equipped with anti-noise ability, and often deliver low performance when learning accurate hyperplane normal vectors from noisy data. To attack this issue, an anti-noise quantum support vector machine algorithm is developed in this paper. Specifically, a weight factor is first embedded into the hinge loss, so as to construct the objective function of anti-noise support vector machine. And then, an alternative iterative optimization strategy and a quantum circuit are designed for solving the objective function, aiming to obtain the normal vector and intercept of the hyperplane that finally divides the data. Finally, the classification and anti-noise effect of the algorithm are verified on artificial dataset and public dataset. Experimental results show that the proposed algorithm is efficient, yet maintains stable accuracy in noisy data.

DOI
10.1109/tc.2024.3416619

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Noisy data is ubiquitous in quantum computer, greatly affecting the performance of various algorithms. However, existing quantum support vector machine models are not equipped with anti-noise ability, and often deliver low performance when learning accurate hyperplane normal vectors from noisy data. To attack this issue, an anti-noise quantum support vector machine algorithm is developed in this paper. Specifically, a weight factor is first embedded into the hinge loss, so as to construct the objective function of anti-noise support vector machine. And then, an alternative iterative optimization strategy and a quantum circuit are designed for solving the objective function, aiming to obtain the normal vector and intercept of the hyperplane that finally divides the data. Finally, the classification and anti-noise effect of the algorithm are verified on artificial dataset and public dataset. Experimental results show that the proposed algorithm is efficient, yet maintains stable accuracy in noisy data.
Noisy data is inherent in quantum computing and significantly affects the performance of many quantum machine learning algorithms. Conventional Quantum Support Vector Machines (QSVMs) often lack built-in mechanisms to handle noise, which can lead to unreliable decision boundaries under noisy conditions. To address this challenge, this work proposes a Hybrid Ensemble Anti-Noise QSVM framework designed for robust classification. The proposed approach integrates neural network–based feature extraction to generate noise-resilient representations with an Anti-Noise QSVM that incorporates a sample-weighted hinge loss to reduce the influence of noisy or mislabeled samples. Furthermore, an ensemble voting mechanism combines the Anti-Noise QSVM with multiple classical classifiers to enhance stability and generalization. The framework is structured to support evaluation on synthetic and real-world datasets, including image, biomedical, and network intrusion data, under various noise conditions such as Gaussian, impulse, and label noise using quantum simulators. This hybrid quantum–classical design aims to improve robustness, scalability, and adaptability compared to conventional QSVM-based approaches.
In the objective world, how to deal with the complexity and uncertainty of big data efficiently and accurately has become the premise and key to machine learning. Fuzzy support vector machine (FSVM) not only deals with the classification problems for training samples with fuzzy information, but also assigns a fuzzy membership degree to each training sample, allowing different training samples to contribute differently in predicting an optimal hyperplane to separate two classes with maximum margin, reducing the effect of outliers and noise, Quantum computing has super parallel computing capabilities and holds the promise of faster algorithmic processing of data. However, FSVM and quantum computing are incapable of dealing with the complexity and uncertainty of big data in an efficient and accurate manner. This paper research and propose an efficient and accurate quantum fuzzy support vector machine (QFSVM) algorithm based on the fact that quantum computing can efficiently process large amounts of data and FSVM is easy to deal with the complexity and uncertainty problems. The central idea of the proposed algorithm is to use the quantum algorithm for solving linear systems of equations (HHL algorithm) and the least-squares method to solve the quadratic programming problem in the FSVM. The proposed algorithm can determine whether a sample belongs to the positive or negative class while also achieving a good generalization performance. Furthermore, this paper applies QFSVM to handwritten character recognition and demonstrates that QFSVM can be run on quantum computers, and achieve accurate classification of handwritten characters. When compared to FSVM, QFSVM’s computational complexity decreases exponentially with the number of training samples.
Quantum Machine Learning is an active research field where the power of quantum mechanics is integrated into machine learning algorithms to solve problems that are intractable for classical computers. Quantum support vector machine (QSVM) was one of the first quantum algorithms that got implemented on real quantum hardware. It demonstrated promising outcomes as compared to classical Support vector machine (SVM) through many implementations. However, it encounters challenges in scaling with large datasets and in resource effectiveness when compare to the usage of innovative classical algorithms in the Noisy Intermediate Scale Quantum era. Here is a review of some latest developments of QSVM and discussion on prospects of QSVM application in the future.
Abstract The high-dimensional linear separability of the classic support vector machine is achieved through the kernel method, which maps data to a high-dimensional space. However, the kernel method involves estimating multiple parameters, which reduces the model's computational efficiency. To address this, some related works use quantum kernel estimation to replace the classic kernel method, thus reducing the computational load associated with parameter estimation in quantum support vector machines. Despite these improvements, quantum support vector machines face the challenge of establishing correlations between different data points through quantum entanglement to effectively capture the distribution characteristics of the data. Consequently, the model's accuracy is low when performing regression analysis on large datasets with complex distributions. To address this issue, an improved quantum backpropagation algorithm is introduced, utilizing controlled-Z gates to entangle qubits representing different data points. Additionally, to enhance the entanglement between qubits, the absolutely maximally entangled state is employed to further optimize the quantum backpropagation algorithm. This enhancement enables the algorithm to better capture the distribution characteristics of the data. Building on this, the quantum support vector machine model is improved to overcome the shortcomings of the existing model. A new algorithm is proposed, and the parameter count of the new algorithm's circuit is analyzed. Experimental results demonstrate that optimizing the quantum backpropagation algorithm to improve the quantum support vector machine leads to higher accuracy in regression analysis on real-world problems. Specifically, strengthening the degree of quantum entanglement makes the model more capable of capturing the distribution characteristics of complex datasets, resulting in more accurate fitting outcomes.
The current development of Support Vector Machines (SVM) has reached a bottleneck, with issues such as long training times and weak interpretability when dealing with large-scale, multi-dimensional data. This paper introduces the concept of Quantum Support Vector Machines (QSVM) and achieves efficient solutions through quantum algorithms such as the HHL algorithm. The research designs a computational architecture that combines classical and quantum computing, utilizing the Pauli decomposition of Hermitian matrices to simulate the quantum simulation of Hamiltonian quantities and implementing the quantum simulation of unitary operators. Based on the conclusions, a complete quantum linear solver circuit is designed, achieving exponential growth in computational complexity. Experiments using the Iris dataset demonstrate the excellent classification performance of QSVM, which outperform classical SVM in classification accuracy, computational time complexity, and memory requirements. More efficient quantum mapping algorithms and quantum circuit optimization methods are implemented, providing new ideas and methods for the application of SVM to large-scale datasets.
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.