Optimizing Quantum Support Vector Machines using ZX-Calculus

Resumo

Quantum Support Vector Machines (QSVMs) represent a promising approach for quantum-accelerated machine learning, but their implementation on Noisy Intermediate-Scale Quantum (NISQ) hardware is constrained by deep circuits and high gate counts, which intensify noise accumulation and decoherence. To mitigate these limitations, ZX-Calculus is employed, a diagrammatic tool that applies mathematical transformations (such as spider fusion, identity removal, and local complementation) to reduce the number of operations without compromising circuit functionality. This reduction in complexity makes QSVMs more viable for execution on noisy intermediate-scale quantum (NISQ) devices. In Quantum Machine Learning (QML), QSVMs stand out for using quantum feature mapping, enabling a rich representation of data. Unlike classical SVMs, which explicitly define the kernel function, QSVMs utilize quantum circuits to implicitly compute kernel values, making it possible to represent complex feature spaces. However, execution is still affected by circuit depth and entanglement overhead. ZX-Calculus has emerged as a powerful technique for optimizing quantum circuits by representing them as tensor networks and enabling algebraic transformations that simplify their structure. Although previous studies have used this approach to analyze barren plateaus and optimize circuit architectures, few works apply it specifically to reduce feature mapping complexity in QSVMs. This study fills that gap by applying ZX-Calculus to optimize quantum kernels, reducing gate overhead without degrading classification accuracy. [...]