With the increasing trend of quantum computing in recent years, many quantum machine learning (QML) models are being widely used to replace the classical models for solving complex classification problems as the latter struggles with nonlinearly separable datasets. One such quantum algorithm is the Pegasos-Quantum Support Vector Classifier ( \(P-QSVC\) ) which solves the binary classification problems more efficiently or comparable to its classical counterpart by leveraging quantum computing fundamentals. Quantum walks are nonlinear quantum computational frameworks that enhance performance by utilizing quantum mechanical principles such as superposition and interference. In our approach, we make use of the coined quantum walk in a two-dimensional lattice to optimize the functionality of the \(P-QSVC\) in solving the XOR problem, a nonlinear separable problem. Nonlinearly separable problems are a class of classification problems where a single straight line cannot separate the data points from differed classes. The XOR problem is an elementary example of this category, and finding an effective solution for XOR constitutes a critical step toward addressing more such nonlinearly separable problems. Our proposed model, the Quantum Walk Optimized Pegasos-Quantum Support Vector Classifier ( \(QW-PQSVC\) ) efficiently classifies the binary nonlinearly separable XOR dataset by minimizing the \({\mathcal {L}}\) oss function and maximizing the classification accuracy of the model using an iterative process. Additionally, we provide the values of the parameters used in the qubit encoding and also the quantum kernel for increasing the classification accuracy of the test points. Using this optimization approach, we achieved the classification accuracy of 99% alongside other metrics such as precision, F1-score and recall scores close to 99% as compared to the 95% accuracy of the \(P-QSVC\) . We further experimented using the fivefold cross-validation, to ensure the generalization and reduce the risk of overfitting or underfitting our model thereby validating the optimization process.
