Title:Oral: Quantum algorithms for solving a drift-diffusion equation

We present three quantum methods for solving a multi-dimensional drift-diffusion differential equation. These are quantum linear systems solver, the quantum random walk and the quantum Fourier transform methods. The complexity of these methods are compared to each other and their classical counterparts. We find that the quantum Fourier transform provides quantum computational advantage when solving for a fixed time. We apply the multidimensional amplitude estimation process to each of the methods to extract the whole probability distribution from the quantum computer.