Electronic structure simulations for batteries and fuel cells using a quantum computer

Abstract

The design of novel technologies for producing, transferring and storing energy, requires an accurate understanding of molecular structures across a wide range of spatiotemporal scales, from microscopic systems governed by the laws of quantum mechanics to mesoscopic continuum models that are employed to investigate the thermodynamic efficiency of batteries, solar and fuel cells. In the era of Noisy Intermediate-Scale Quantum (NISQ) computers, meaningful calculations of electronic structure are restricted to a few qubits [1]. In order to reduce the complexity of the original molecular Hamiltonian and identify the most relevant subspace for determining ground state energies, orbital optimization and preliminary quantum chemistry calculations are often employed. In order to keep the qubit count as low as possible and increase the accuracy of energy estimates, a familiy of hybrid algorithms that leverage additional measurements on the quantum processor without an increase in the size of the quantum register have gained popularity. In particular, quantum subspace expansion (QSE) techniques [2] take into account excitations upon a reference state and measurements on the quantum computer are performed to build the matrix elements that conform a generalised eigenvalue problem (GEVP) on this restricted subspace. These methods require a regularization procedure of the GEVPs matrices that are built via noisy measurements, which can lead to the presence of spurious eigenvalues. In this work, we investigate the sensitivity to noise of subspace expansion techniques when implemented on NISQ hardware such as the IBM System One quantum computer. In addition, we provide practical limitations to the use of bayesian methods [3] that in conjunction with a characterization of the noise, can be employed to regularise the GEVP matrices that are built from noisy measurements. [1] McArdle, S. et al. Rev. Mod. Phys., 92, 015003 (2020) [2] Takeshita, T. et al. Phys. Rev. X, 10, 011004 (2020) [3] Caleb Hicks and Dean Lee, Phys. Rev. Research 5 (2023)