Optimizing the Quantum Circuit of Quantum K-Nearest Neighbors (QKNN) Using Hybrid Gradient Descent and Golden Eagle Optimization Algorithm

This study concentrates on the enhancement of the quantum circuit pertaining to Quantum K-Nearest Neighbors (QKNN), which is a fundamental algorithm within the domain of quantum machine learning, through the implementation of a hybrid optimization methodology that integrates Gradient Descent with the Golden Eagle Optimization Algorithm (GEOA). QKNN harnesses the capabilities of quantum computing to process high-dimensional datasets with enhanced computational efficiency and precision; however, its effectiveness is frequently compromised by inadequate quantum circuit parameters and elevated noise levels present in near-term quantum devices. The proposed hybrid optimization methodology augments Quantum K-Nearest Neighbors (QKNN) through the amalgamation of the global search capabilities inherent in Golden Eagle Optimization (GEO) and the localized refinement efficacy provided by Gradient Descent (GD). This collaborative interplay culminates in expedited convergence (40 iterations), elevated classification accuracy (97.2 %), diminished circuit complexity (42 quantum gates), and enhanced resilience against gate noise (fidelity: 0.983). In contrast to conventional optimization techniques such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Simulated Annealing (SA), our proposed methodology demonstrates superior efficacy by optimizing quantum distance computation, entanglement strategies, and circuit depth, while simultaneously attenuating the effects of gate noise.