Variational Quantum Algorithms for Continuum Modelling of Batteries

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Abstract

Quantum computing is becoming relevant to energy science for more accurate calculations in quantum chemistry and in materials discovery with quantum machine learning methods. However, it is also applicable to cell models thanks to recent works solving nonlinear partial differential equations (PDEs). Various methods have been recently proposed, including fault-tolerant quantum linear systems algorithms (QLSAs) for linear and nonlinear PDEs. In practice, however, these fault-tolerant algorithms do not yet give a quantum advantage. On current noisy intermediate-scale quantum (NISQ) devices, these algorithms are affected by strong limitations on the depth of the quantum circuits that can be coherently executed. On NISQ devices, variational quantum algorithms (VQAs) have become a popular approach to solving PDEs. Many algorithms have been proposed that solve one time step at a time, which inherently presents a limitation to the scalability and accuracy. In our paper, we combine quantum nonlinear processing units (QNPUs) with the Feynman-Kitaev Hamiltonian to achieve a spacetime solution instead, and apply it to the nonlinear Burgers equation. We find the ground state of this Hamiltonian using an adaptive optimization procedure to avoid barren plateaus. Here, we also apply this method to an adapted version of the single particle model with electrolyte (SPMe).

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• Variational Quantum Algorithms for Continuum Modelling of Batteries. (deposited 22 Jun 2026 07:50) [Currently Displayed]