A Comprehensive Review of Quantum Annealing for Combinatorial Routing Problems

Abstract

Quantum computing has grown as a transformative paradigm for addressing combinatorial optimisation issues, which are common in diverse fields such as logistics, finance, and network architecture. This paper examines current progress in quantum computing methodologies and their application to combinatorial optimisation, highlighting emerging trends in algorithm development, hybrid quantum-classical strategies, and hardware developments. Significant advancements include the optimisation capabilities of quantum annealing, enhancements in gate-based quantum algorithms like the Quantum Approximate Optimization Algorithm (QAOA), and the amalgamation of machine learning with quantum optimisation frameworks. Recent studies emphasise scalability issues, error correction methods, and the increasing accessibility of quantum cloud services. This study offers a thorough analysis of cutting-edge techniques, applications, and prospective research avenues, elucidating the revolutionary impact of quantum computing on complicated optimisation challenges.