Potential Energy Savings from Quantum Computing-Based Route Optimization

We investigate the potential of the Quantum Approximate Optimization Algorithm (QAOA) for reducing energy consumption in route planning, a key challenge in logistics due to the NP-hard nature of the Traveling Salesman and Vehicle Routing Problems. By encoding route optimization as a Quadratic Unconstrained Binary Optimization (QUBO) problem and implementing QAOA circuits at depth p = 3-5 alongside classical baselines of Simulated Annealing (SA) and Genetic Algorithms (GA), we perform systematic benchmarks on Euclidean graphs of sizes N = 5, 10, and 20. Our results demonstrate that QAOA attains higher solution quality with approximation ratios of 0.953 (N = 5), 0.921 (N = 10), and 0.903 (N = 20), outperforming SA and GA by 2.7-4.4%. Wall-clock runtimes for QAOA are 2-3x faster than SA across all tested sizes, and energy consumption measurements reveal a three-order-of-magnitude reduction, remaining in the picojoule range versus nanojoules for classical methods. Translating these gains to real-world logistics suggests an 8.2% improvement in routing efficiency could save approximately 2.62 EJ of fuel annually in the U.S., avoiding nearly 1.94 x 10^8 tonnes of CO2 emissions. These findings highlight QAOA's promise as a fast, energy-efficient optimizer for sustainable logistics applications and underscore its potential role in next-generation fleet-management systems.