Towards Quantum Simulations of Lithium Diffusion in Solid State Electrolytes for Battery Applications

Advancing battery materials is crucial for sustainable infrastructure, EVs and renewable energy storage. By achieving polynomial scaling for exact electronic structure simulations of materials, quantum computing could emerge as an invaluable tool in this field. In this work, we address two fundamental aspects related to the application of quantum algorithms to lithium diffusion in solid state electrolytes, which have the potential to significantly improve safety and performance of current battery technologies. First of all, we discuss the need for the higher level of accuracy provided by quantum computing. Classical computational methods routinely applied to compute the properties of solid state electrolytes are based on semi-local approximations of density functional theory (DFT). Considering cluster models representative of the properties of the bulk Li<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</inf>GeP<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</inf> (LGPS) electrolyte, we benchmark several functionals, including state-of-the-art hybrid approximations and compare the results to high-level wavefunction methods. The classical results for lithium diffusion barriers exhibit a variability exceeding the chemical accuracy threshold required for experimentally relevant precision, underscoring the necessity for exact quantum solutions as a reference. Secondly, we perform quantum simulations for lithium diffusion barriers using small active spaces of the cluster models and use those results to extrapolate the minimal resources required for a full simulation of bulk LGPS. Specifically, the variational quantum eigensolver (VQE) with a quantum number preserving ansatz and the quantum Krylov (qK) method are considered. The resource estimations for VQE show that a few hundred qubits and less than one million two-qubit gates could be sufficient to simulate LGPS. For qK the number of required two-qubit gates increases by orders of magnitude. However, for large models it should also be considered that qK avoids the complex non-linear optimization problem involved in VQE. Future advancements in quantum algorithms will be essential for bringing simulations of materials closer to realization.