Matrix Geometric Solutions with Quantum Speed-up for EV Battery Swapping Systems

Electric vehicle (EV) charging and battery swapping system is the future of urban transportation. Such a system can be modeled as a quasi-birth-and-death process and its stationary distribution could be numerically obtained from the classical cyclic reduction (CR) algorithm. We consider utilizing quantum algorithms to accelerate the computation in solving a system of linear equations and derive the exact solution of matrix-geometric form. We further analyze the steady-state behavior of the system and present useful insights for future EV infrastructure planning.