Quantum Approaches to Urban Logistics Solve Traveling Salesman Problem with Real-World Constraints

The challenge of efficiently solving the Traveling Salesman Problem, a critical issue in logistics and transportation, continues to drive innovation in optimisation techniques. Researchers, including F. Picariello, G. Turati, and R. Antonelli, alongside colleagues, now demonstrate the potential of quantum computing to tackle this complex problem under realistic conditions. Their work investigates the Approximate Optimisation Algorithm, a hybrid quantum-classical approach, formulated to incorporate real-world logistical constraints such as vehicle capacity and time windows, while remaining compatible with current quantum hardware. By proposing a novel method called Clustered QAOA, the team successfully decomposes large, intractable problems into smaller, more manageable sub-problems, significantly improving scalability and paving the way for future applications of quantum computing in large-scale logistics and transportation networks. The study formulates the TSP as a Quadratic Unconstrained Binary Optimization (QUBO) problem, allowing it to be processed by QAOA while incorporating realistic logistical constraints such as vehicle capacity, road accessibility, and time windows. To enforce the crucial one-city-per-step constraint, researchers implemented a Grover-inspired mixer, a specific quantum circuit designed to guide the optimization process. Recognizing the limitations of available qubits, the team pioneered a clustering-based QAOA (Cl-QAOA) method, decomposing large TSP instances into smaller, more manageable sub-problems using classical machine learning algorithms. This hybrid approach enables optimization even with a limited number of qubits, and a comprehensive temporal scaling analysis evaluated its practical applicability and scalability. Researchers meticulously evaluated solution quality and computational time across different algorithms and configurations, utilizing both synthetic benchmarks and real-world datasets to validate the approach, demonstrating the potential of combining quantum and classical computing to tackle complex logistical challenges.,. Quantum QAOA Solves Constrained Traveling Salesman Problem Scientists have achieved a breakthrough in solving the Traveling Salesman Problem (TSP) using the Quantum Approximate Optimization Algorithm (QAOA), demonstrating its potential for realistic logistical challenges. The work focuses on optimizing routes while incorporating crucial real-world constraints such as vehicle capacity, road accessibility, and time windows. Researchers implemented a Grover-inspired mixer within the QAOA framework to enforce the fundamental constraint of visiting each city only once, ensuring a valid route is always considered.

The team formulated the TSP as a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling its efficient implementation on quantum hardware. To overcome limitations in qubit availability, scientists developed Cluster-QAOA, a hybrid approach combining classical machine learning with QAOA, decomposing large TSP instances into smaller, more manageable sub-problems. Researchers developed a QUBO-based formulation that efficiently encodes these constraints without demanding excessive quantum resources, and implemented a novel mixer designed to enhance convergence towards viable solutions. Experiments conducted on both artificially generated and real-world datasets reveal that QAOA consistently identifies optimal solutions for problem instances up to a certain size, achieved with shallow quantum circuits and a limited number of measurements.

The team further advanced scalability by proposing Clustering QAOA, a hybrid approach that decomposes large problems into smaller, more manageable sub-problems, and results indicate that increasing the maximum sub-problem size generally improves solution quality. The method exhibits a promising linear scaling trend, suggesting a potential computational advantage over classical algorithms for large-scale problems, establishing a practical pathway for applying QAOA to real-world optimization challenges. 👉 More information 🗞 Quantum Approaches to Urban Logistics: From Core QAOA to Clustered Scalability 🧠 ArXiv: https://arxiv.org/abs/2512.10813 Tags: Rohail T. As a quantum scientist exploring the frontiers of physics and technology. My work focuses on uncovering how quantum mechanics, computing, and emerging technologies are transforming our understanding of reality. I share research-driven insights that make complex ideas in quantum science clear, engaging, and relevant to the modern world. Latest Posts by Rohail T.: Cryogenic Muon Tagging System with Kinetic Inductance Detectors Monitors Radiation for Quantum Processors December 12, 2025 Hybrid Quantum-Classical Methods Model Electron-Phonon Systems, Enabling Study of Holstein Chains and Quenched Disorder December 12, 2025 Distributed Quantum Computing Achieves Advantage with Slow Interconnects and up to Five Times Longer Entanglement Generation December 12, 2025