Quantum Computing for Battery Materials Modeling

Previous work of our group proposed an efficient optimization method for sampling the ground state of ionic materials, based on a fully interacting Coulomb energy model [1,2]. Using lithium cobalt oxide (LCO) and lithium iron phosphate (LFP) as benchmark models, we have tested and implemented two different quantum computing approaches: quantum annealing on D-Wave Hardware and the gate-based quantum approximate optimization algorithm (QAOA). This project will focus on gate-based quantum circuit approaches. As this research is in its initial phase, the choice of the quantum algorithm is still under  discussion. We aim to develop an electro-ionic model Hamiltonian based on the extended Hubbard model for ground state estimation.  The proposed methodology utilizes a second quantization approach, where each qubit represents a specific spin-orbital in the chosen basis, and the computational state tracks their occupancy. This requires N qubits to represent N orbitals, allowing for straightforward state preparation but leading to higher qubit count compared to first quantization approaches. The latter is "particle-centric", where registers store only the binary indices of the n electrons. While this reduces the qubit cost to O(n log (N))[4]. First quantization necessitates a complex antisymmetrization step, implemented via sorting networks and Givens rotations, that significantly increases circuit depth. By choosing second quantization, we prioritize simpler initial state preparation while planning to mitigate the qubit count by utilizing approximation techniques in combination with existing quantum algorithms. Fermionic operators are then mapped to Pauli gates using standard transformations such as Jordan-Wigner or Bravyi-Kataev for circuit execution.

This project follows a structured pipeline spanning theoretical circuit construction, classical simulation, and quantum hardware implementation. First, we aim to provide a fully worked-out quantum circuit that translates our model Hamiltonian into a gate-based architecture for execution on a quantum circuit. Next, our future plans consist of simulating the circuit classically to validate the formulation and benchmark ground-state energy predictions of the unit cell against established classical results from DFT. Finally, the algorithm will be executed on NISQ-era quantum hardware using scaled-down circuits to assess practical feasibility, with particular attention to the effects of noise and gate errors on long-range interactions. The goal is to assess the robustness of the proposed approach and its scalability to larger and more complex battery supercells on future fault-tolerant quantum devices.

We aim to develop quantum-oriented techniques for ground state energy estimation for realistic models of battery materials. As we are currently in the initial phase of this research, the application potential of our approach is anticipated to lie in its ability to bridge the gap between current NISQ-era limitations and the requirements for high-fidelity industrial materials science. To increase scalability and maximize the quantum utility of our algorithm, we could use classical methods as initial predictions for our parameters of the extended Hubbard model, then the quantum processor to account for strong electron correlations. We could opt for subspace projection or hybrid quantum-classical techniques, like active spaces or quantum circuit cutting, to keep the qubit count within a range that is compatible with early fault-tolerant architectures.