Quantum Path Integral Approach for Vehicle Routing Optimization With Limited Qubit

The Vehicle Routing Problem (VRP) is a crucial combinatorial optimization problem in transportation, logistics, and supply chain management. Quantum computing has gained interest in solving complex optimization issues. This review paper proposes a novel approach that combines quantum computing principles with the Feynman path integral formulation to address the VRP. The paper focuses on limited qubits and how quantum algorithms can circumvent this limitation. Conventional methods, such as Lagrangian and combinatorial optimization, require computational time to solve complex atomic-scale problems. The path integral formulation with the first Born approximation method offers a more elegant explanation of quantum computing. The algorithm investigates quantum system dynamics using the Schrodinger wave equation and computes probability amplitude distributions for optimal vehicle routing techniques. This work will take advantage of entanglement and interference effects for heuristic sampling of high-quality solutions, making the Quantum Path Integral Approach (QPIA) a promising study environment for investigating quantum circuits and algorithms in routing problems with constrained qubits.