Simulations of electrochemical materials and systems accelerate technological progress, but are still limited by computational power. In particular, quantum computing offers prospects for higher resolutions, due to the exponential amount of data that can be stored in a quantum state. As current quantum computers are still noisy, we consider a hybrid quantum-classical algorithm, that divides the problem into smaller computational tasks. We describe how to implement such an algorithm for non-linear partial differential equations, the Feynman-Kitaev Hamiltonian, in a scalable way for an electrochemical system. We show how it can evaluate general electrochemical models and present a quantum simulation of the Single Particle Model with electrolyte (SPMe) as the first quantum simulation of a battery cell.
Simulations of electrochemical materials and systems accelerate technological progress, but are still limited by computational power. In particular, quantum computing offers prospects for higher resolutions, due to the exponential amount of data that can be stored in a quantum state. As current quantum computers are still noisy, we consider a hybrid quantum-classical algorithm, that divides the problem into smaller computational tasks. We describe how to implement such an algorithm for non-linear partial differential equations, the Feynman-Kitaev Hamiltonian, in a scalable way for an electrochemical system. We show how it can evaluate general electrochemical models and present a quantum simulation of the Single Particle Model with electrolyte (SPMe) as the first quantum simulation of a battery cell.
Mathematical models of electrochemical systems such as batteries or fuel cells consist of sets of coupled nonlinear partial differential equations. We describe how variational quantum algorithms (VQAs) can be used to solve these equations on a quantum computer [1]. VQAs are hybrid quantum-classical algorithms, where a cost function is calculated on a quantum computer and its parameters are optimised classically. We present a spacetime representation, inspired by the Feynman--Kitaev Hamiltonian [2], where the solution to a PDE at all times is obtained by minimising just one function. [1] A.J. Pool, A.D. Somoza, C. Mc Keever, M. Lubasch, B. Horstmann, Phys. Rev. Res. 6 (2024), 3, 033257 [2] S. Barison, F. Vicentini, J.I. Cirac, G. Carleo, Phys. Rev. Res. 4 (2022), 4, 043161
The material design for batteries in industry and research is greatly facilitated by computational simulations on classical computers. A central tool are numerical solvers for Partial Differential Equations (PDEs), which arise as the transport equations of ions in the continuum-model of battery cells. However, these methods reach their limits when simulating the fine-grained heterogeneous structures of porous electrodes. Quantum computing is a promising candidate to achieve an advantage in scalability through the exponential growth of representable states. On current NISQ-devices promising candidates are Variational Quantum Algorithms (VQAs) to solve nonlinear PDEs. Experimental results demonstrate the capabilities of both space-time encodings with Quantum Non-linear Processing Units (QNPUs) and spectral feature mappings with Differentiable Quantum Circuits (DQCs).
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).
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 Li10GeP2S12(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.
The urgent need for high-performance, sustainable electric vehicle (EV) batteries has driven the exploration of advanced computational methods to accelerate material discovery. Traditional approaches, such as Density Functional Theory (DFT) and Hartree-Fock, face inherent limitations in simulating the complex quantum behaviors of novel battery materials. This paper introduces a pioneering framework leveraging quantum computing, specifically the Variational Quantum Eigen solver (VQE), to overcome these challenges and optimize solid-state battery materials. We focus on Lithium Thiophosphate (Li3PS44), a promising electrolyte for next-generation batteries, and demonstrate how quantum simulations can provide a deeper understanding of electronic structures and electrochemical reactions at an unprecedented level of precision. By benchmarking quantum results against classical methods, we highlight the transformative potential of quantum algorithms to capture intricate electron correlations and reaction dynamics, offering more accurate predictions for material performance. Our findings suggest that quantum computing not only offers a significant leap in the accuracy of battery material simulations but also paves the way for scalable, data-driven optimization of next-generation energy storage systems.
Sodium-ion batteries (SIBs) are becoming progressively more prevalent as a feasible substitute for lithium-ion batteries (LIBs) due to the rising need for affordable and sustainable energy storage on a worldwide scale. Because sodium is abundant and relatively inexpensive, SIBs seem appealing. However, the intricacy of their electrochemical properties, which includes ion transport, intercalation kinetics, and thermal characteristics poses a hindrance to their broad adoption. Current available classical algorithms struggle with scalability, nonlinearity, and computational intensity of electrical vehicle (EV) battery models. This paper proposes a quantum-assisted state estimation framework tailored to enhance predictive accuracy and computational robustness of battery state estimation using a hybrid quantum-classical model. Our approach proposes utilizing simulated data derived from a physics-based pseudo-twodimensional (P2D) electrochemical model to train and validate a variational quantum circuit (VQC) designed for state of charge (SOC) and voltage prediction. Although no quantum hardware execution is performed in this study, rather this work introduces a framework and simulation-ready methodology for future deployment. The results show theoretical viability and potential for superior (hybrid) quantum performance compared to classical-only models, laying the groundwork for quantumenhanced battery management systems.