Quantum Algorithm for Poisson Equation with Inhomogeneous Media

Quantum computer has attracted much attention from academy and industry due to the marvelous acceleration compared with classical computers. A quantum computing algorithm for Poisson equations with inhomogeneous media is presented here. The original equation is discretized with square grids and transformed into linear equations using finite difference method. Then the quantum algorithm for solving sparse matrix equations is applied to the discretized Poisson equation. The quantum algorithm can achieve O(log N) complexity. Numerical simulations verify the accuracy of such algorithm.