Quantum Algorithms for Heterogeneous PDEs: The Neutron Diffusion Eigenvalue Problem
The research develops a hybrid quantum-classical method to solve neutron diffusion eigenvalue problems in heterogeneous media. It uses finite element methods combined with quantum linear system solvers, specifically fast inversion and preconditioning, to find the critical eigenvalue ($k$). This approach offers a polynomial speedup over classical uniform FEM for determining nuclear criticality.