In this paper, we propose a novel quantum computing approach to solve the real-world problem of optimizing transportation in bustling Kathmandu city. The transportation system in Kathmandu is chaotic, with no central authority controlling the transportation. We leverage this chaotic feature in our quantum optimization procedure. Characterized by quantum chaos theory, the Wigner-Dyson distribution has surfaced as the most effective bus spacing distribution for a bus driver to maximize their profit. We investigate the statistical properties of the buses with real-time GPS bus location data and optimize bus spacing and interval distribution around the 27 km circular ring road in Kathmandu. Using tools like quantum simulation, eigenvalue distributions, and output wave function analysis, we show that such optimal bus spacing distribution could be achieved.