Variational quantum algorithms for continuum modelling of batteries

Kurzfassung

We present variational quantum algorithms (VQAs) for continuum models in electro-chemical energy-storage-systems, focusing on transport equations in batteries. Our method uses a space-time encoding with time evolution based on the Feynman-Kitaev Hamiltonian, as introduced in [1]. We show how to implement the non-linear terms of the transport equations and discuss efficient quantum circuits to evaluate the terms of this Hamiltonian, and to realize suitable boundary conditions. Further, we present an adaptive optimisation strategy to find the ground state, which represents the solution to a differential-algebraic system of equations. [1] Pool et al. Phys. Rev. Research 6, 033257 (2024).