Modelling super-diffusion in urban human mobility: a quantum walk approach

Super-diffusion in urban human mobility refers to the faster-than-linear increase in the mean squared displacement (MSD) of the mobility collective over time. Accurate modeling of super-diffusion in urban human mobility is a key focus in various research fields and industries. However, there are few urban human mobility models that can capture super-diffusion. To address this gap, this paper proposes a quantum walk-based urban human mobility model (UHM-QW). In quantum walks, the spread of a walker exhibits super-diffusion properties. UHM-QW generates mobility patterns with varying diffusion rates by quantum walks and models the collective super-diffusion as a weighted combination of important mobility patterns. Experiments show that UHM-QW can accurately reproduce the super-diffusion process and its temporal fluctuation characteristics. Compared to the reference models (Random Walk, SeqGAN, LSTM-TrajGAN), UHM-QW achieves greater fit accuracy (R²), better retains temporal structure (NDTW-t), and captures fluctuation details (NDTW-r). Analysis of important mobility patterns reveals that faster-diffusing collectives are driven by faster diffusion-rate patterns, while those with greater variability arise from patterns with substantial differences in diffusion-rates. Additionally, a single dominant mobility pattern effectively reproduces the super-diffusion process, reducing the model's complexity and enhancing its interpretability. In conclusion, this paper reveals the correspondence between quantum walk dynamics and human mobility patterns, providing a new perspective for mining human mobility laws in cities.