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Variational quantum algorithm for anion exchange across an electrolyzer membrane

Year: 2026
Type: article
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 ion across a two-layer membrane in an alkaline electrolyzer, where the concentration of OH − ion determines the chemical stability for longer time periods. We use 16 to 64 grid points across the membrane, resulting from n = 4 to 6 data qubits for the ideal statevector and shot-based quantum simulations implemented using Qiskit. 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 variational quantum algorithms (VQA) method. We demonstrate the applicability of the quantum algorithm to a problem with nontrivial boundary conditions and jump conditions of the diffusion constant and outline possible extensions of the proof-of-concept application case of quantum computing. Our simulations show that pronounced hydroxide-ion concentration gradients, and thus chemical instabilities, can occur only when the ratio of diffusivity in both layers of the membrane exceeds approximately 50.
DOI: 10.1103/149q-4z6s
Language: English
Open Access status: hybrid
OpenAlex ID: W7165123813
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Cites: 51
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Related to: 10