Structural Impact of Urban Topologies on Quantum Approximate Optimization: A Comparative Study of Planned vs. Organic Road Networks

Quantum Physics [Submitted on 13 Mar 2026] Structural Impact of Urban Topologies on Quantum Approximate Optimization: A Comparative Study of Planned vs. Organic Road Networks Abdul Sami Rao, Roha Ghazanfar Khan, Shumaila Ashfaq The performance of shallow-depth quantum optimization algorithms is known to depend strongly on problem structure, yet the role of real-world network topology remains poorly understood. In this work, we study how urban graph structure influences the behaviour of the Quantum Approximate Optimization Algorithm (QAOA) at depth p=1. Using street-network subgraphs extracted from two cities in Pakistan with contrasting urban designs - a planned city (Islamabad) and an organically grown city (Lyari) - we analyse probability concentration, approximation quality, and performance variability on the minimum vertex cover problem. By comparing classical brute-force solutions with QAOA outcomes, we show that planned topologies yield more reliable convergence, while organic networks exhibit higher variance and a greater tendency toward trivial solutions. Our results suggest that urban structure primarily affects the robustness rather than the average quality of shallow QAOA solutions, highlighting the importance of higher-order structural heterogeneity in shaping low-depth quantum optimization landscapes. This research is vital because it bridges the gap between abstract quantum theory and the chaotic reality of our physical world, proving that the way we build our cities directly impacts our ability to optimize them. By identifying how "topological DNA" influences algorithmic success, this work enables the development of more resilient quantum solutions for critical infrastructure, such as smart power grids and emergency response routing. Ultimately, these insights benefit society by paving the way for more efficient, data-driven urban management that can reduce resource waste and improve the quality of life in both planned and organically growing metropolitan areas. Comments: 12 pages, 4 graphs Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.12601 [quant-ph]   (or arXiv:2603.12601v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.12601 Focus to learn more Submission history From: Abdul Sami Rao [view email] [v1] Fri, 13 Mar 2026 03:07:53 UTC (999 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)