Quantum algorithms to solve partial differential equations in battery modelling

Kurzfassung

In the mathematical modelling of electrochemical systems like batteries, systems of coupled partial differential equations are used. Their numerical solution is limited by the available computational resources. We present variational quantum algorithms to solve partial differential equations. Different methods based on the ground state estimation of a Feynman-Kitaev Hamiltonian (Barison, S. et al. Phys. Rev. Res. 4, 043161) and Differentiable Quantum Circuits (Kyriienko et. al. Phys. Rev. A 103, 052416) are explored. In both methods the system can be evaluated in space and time simultaneously. We will show examples of linear and nonlinear partial differential equations solved on simulators and demonstrate that current quantum computers are capable of accurately reproducing the exact results. The scaling of these quantum algorithms with the problem size is discussed.