Optimizing Quantum Support Vector Machines using ZX-Calculus

Quantum Support Vector Machines (QSVM) employ quantum kernels for classification tasks. This study explores circuit optimization techniques using ZX-Calculus to reduce the computational cost of QSVM implementations while preserving classification accuracy. By applying ZX-diagram rewriting techniques, we achieve an average 82% reduction in gate count and 91.3% reduction in circuit depth, with maximum reductions of 87% and 95%, respectively. Despite these simplifications, accuracy remains stable at 0.900, except for a minor drop to 0.867 in specific configurations. These results show that ZX-Calculus simplifies QSVM circuits, reducing resource overhead without affecting predictive performance.