Quantum algorithm and its implementation for solving partial differential equations

Abstract

Partial differential equations (PDEs) play an important role in engineering since various physical phenomena can be well described by PDEs. The key problems in solving PDEs are memory usage and computational time when the size of the system of interest grows. Given the potential of quantum computing, we propose a quantum algorithm for solving PDEs based on the Hamiltonian simulation, which is well known as the possible application of quantum computing for physical simulation. First, we review the method of linear combination of Hamiltonian simulation and propose its implementation via a tensor network technique. Second, we discuss how to deal with the spatially varying physical constants via a logic minimizer technique. Finally, we provide numerical experiments to demonstrate our proposed method.