Figure from https://arxiv.org/pdf/2012.09265

I have been working on designing and benchmarking a variational quantum algorithm for solving PDEs, originally inspired by Lubasch et al. (https://arxiv.org/abs/1907.09032). The algorithm uses a hybrid classical-quantum approach with the finite difference/finite element method for solving both linear and nonlinear PDEs. I have worked on various equations, including the heat equation, nonlinear Poisson equation, Black-Scholes equation, and Navier-Stokes equation using this method.

This is my ongoing research project. More details available upon request.