Advancing Combinatorial Optimization Using Quantum Mechanics: QAOA and Christofides Algorithm Integration

Abstract

Quantum mechanics has paved the way for ground-breaking advancements in computational methodologies, especially in addressing combinatorial optimization challenges. This paper explores the potential of integrating the Quantum Approximate Optimization Algorithm (QAOA) with the Christofides   Algorithm to solve the Traveling Salesman Problem (TSP). The study examines performance improvements, computational trade-offs, and the hybrid model’s practical implications, focusing on quantum principles applied to minimum weight perfect matching. Detailed analyses of cost functions, scalability, and solution quality provide a fresh quantum-classical perspective on optimization