Robust LS-QSVM Implementation via Efficient Matrix Factorization and Eigenvalue Estimation

Traditional SVM and LSSVM face challenges in handling large datasets due to the exponential increase in computational complexity. Quantum Support Vector Machines (QSVM) based on the HHL algorithm offer a potential solution, but practical implementation in the Noisy Intermediate-Scale Quantum(NISQ) era remains limited. Our work Least Square-QSVM with Ridge Regression(LS-QSVM-RR) addresses these limitations by efficiently decomposing the LSSVM coefficient matrix and encoding it into quantum circuits via a matrix factorization algorithm. We also leverage quantum circuit properties to compute optimal ridge regression constraints by efficient eigenvalue estimation, achieving a balance between prediction accuracy and robustness in QSVM. Our contributions demonstrate the potential of Variational Quantum Algorithm(VQA)-based QSVM simulations and provide insights into handling large condition numbers in LSSVM coefficient matrices.