# Quantum Approaches to Urban Logistics: From Core QAOA to Clustered Scalability

arXiv: https://arxiv.org/abs/2512.10813 · HTML: https://mlsanity.com/paper/2512.10813/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 54 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Graph Clustering with Graph Neural Networks](https://mlsanity.com/paper/2006.16904/) (2020)
- [cuQuantum SDK: A High-Performance Library for Accelerating Quantum Science](https://mlsanity.com/paper/2308.01999/) (2023)
- [Penalty Weights in QUBO Formulations: Permutation Problems](https://mlsanity.com/paper/2206.11040/) (2022)
- [Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation](https://mlsanity.com/paper/2006.00354/) (2020)
- [Quantum Annealing of Vehicle Routing Problem with Time, State and Capacity](https://mlsanity.com/paper/1903.06322/) (2019)
- [Performance of QAOA on Typical Instances of Constraint Satisfaction Problems with Bounded Degree](https://mlsanity.com/paper/1601.01744/) (2016)
- [Feature Selection for Classification with QAOA](https://mlsanity.com/paper/2211.02861/) (2022)
- [Modeling routing problems in QUBO with application to ride-hailing](https://mlsanity.com/paper/2212.04894/) (2022)
- [Solving The Vehicle Routing Problem via Quantum Support Vector Machines](https://mlsanity.com/paper/2308.04849/) (2023)
- [On Circuit Depth Scaling For Quantum Approximate Optimization](https://mlsanity.com/paper/2205.01698/) (2022)
- [Hybrid Quantum-Classical Optimisation of Traveling Salesperson Problem](https://mlsanity.com/paper/2509.26229/) (2025)

## Abstract (arXiv)

The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality solutions within reasonable timeframes. This study investigates the potential of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical method, to solve TSP under realistic constraints. We adopt a QUBO-based formulation of TSP that integrates real-world logistical constraints reflecting operational conditions, such as vehicle capacity, road accessibility, and time windows, while ensuring compatibility with the limitations of current quantum hardware. Our experiments are conducted in a simulated environment using high-performance computing (HPC) resources to assess QAOA's performance across different problem sizes and quantum circuit depths. In order to improve scalability, we propose clustering QAOA (Cl-QAOA), a hybrid approach combining classical machine learning with QAOA. This method decomposes large TSP instances into smaller sub-problems, making quantum optimization feasible even on devices with a limited number of qubits. The results offer a comprehensive evaluation of QAOA's strengths and limitations in solving constrained TSP scenarios. This study advances quantum optimization and lays groundwork for future large-scale applications.