Variational quantum algorithm for anion exchange across electrolyzer membrane

TL;DR

This paper introduces a variational quantum algorithm to solve a one-dimensional diffusion problem with space-dependent diffusivity, relevant for ion exchange in electrolyzer membranes, demonstrating its feasibility with up to 64 grid points.

Contribution

The paper develops a quantum algorithm tailored for diffusion problems with discontinuous coefficients and compares classical optimization methods within the variational quantum approach.

Findings

Successfully modeled diffusion with discontinuities using quantum algorithms.

Demonstrated the algorithm's applicability to realistic boundary conditions.

Analyzed the convergence of different classical optimizers in the VQA context.

Abstract

We present a variational quantum algorithm that solves the one-dimensional diffusion problem with a space-dependent diffusion constant $D(x)$. This problem is relevant for the exchange of hydroxide ions across a multi-layer membrane in an alkaline electrolyzer. We use $16$ to $64$ grid points across the membrane, resulting from $n=4$ to $6$ data qubits for the ideal quantum simulations that are based on the Qiskit software. For these qubit numbers, the depth of the parametric quantum circuit has been chosen to ensure sufficient expressibility. The state preparation requires particular attention since the diffusivity $D$ is piecewise constant in the different layers with discontinuities at the interface. Furthermore, we compare different classical optimization schemes with respect to their convergence in the VQA method. We demonstrate the applicability of the quantum algorithm to a problem with non-trivial boundary conditions and jump conditions of the diffusion constant and outline possible extensions of the proof-of-concept application case of quantum computing.