Quantum Walks on Graphs for Risk-Aware Electric Vehicle Charging Station Recommendation

Charging-station selection must combine reachability, uncertain completion time and operational preferences. We study a station selection rule that combines an upper-quantile score with probabilities obtained from a continuous time quantum walk. We bound the increase in the predicted score. We establish global and local conditions for recommendation stability. An exact condition for a change of station separates the effects of the initial distribution and quantum propagation, while a residual decomposition describes changes in realized performance. Simultaneous conformal bounds provide coverage for the selected station under exchangeable request records with outcomes for every feasible station. A controlled simulation uses energy and connection variability from 70,224 retained commercial sessions and generates roads, queues and loading. On 13,973 chronological test requests, mean completion time is 203.43 min for the quantum rule, 238.04 for nearest-station selection and 203.13 for deterministic total time. Relative to risk-only selection, the full probability preference reduces the mean by 0.90 s: 26 changed choices help and 11 harm. The matched initial-prior and heat controls do not establish a propagation-specific benefit. Simultaneous test coverage is 88.66% at a nominal 90% level.