Quantum Simulations of Battery Electrolytes Using Variational Quantum Eigensolver, Equation‐of‐Motion, and Sample‐Based Diagonalization Methods: Active‐Space Design, Dissociation, and Excited States of LiPF6, NaPF6, and FSI Salts
Sk Mujaffar Hossain, Seung-Cheol Lee, Satadeep Bhattacharjee
ABSTRACT Accurate prediction of excited states in battery electrolytes is crucial for understanding photostability, oxidative stability, and degradation. We employ hybrid quantum‐classical algorithms–the Variational Quantum Eigensolver (VQE) for ground states and the quantum equation of motion (qEOM) for vertical singlet excitations to study , , LiFSI, and NaFSI. Compact active spaces from frontier orbitals were mapped to qubits and reduced via symmetry tapering and commuting‐group measurements to lower sampling cost. Within 10‐qubit models, VQE‐qEOM agrees closely with exact diagonalization, while sample‐based quantum diagonalization (SQD) in larger spaces recovers near‐exact (subspace‐FCI) energies. Spectra show clear anion‐cation trends within the VQE‐qEOM framework: salts have higher first‐excitation energies ( 13.2 eV) and a compact three‐state cluster at 12–13 eV, whereas FSI salts exhibit lower onsets (8–9 eV) with nearly degenerate and states and a higher separated by 1.3 eV. Independent TDDFT calculations yield systematically lower absolute excitation energies but reproduce the same anion‐ and cation‐dependent trends, confirming that the relative ordering and physical interpretation of the quantum results are robust. Replacing with narrows the gap by 0.4–0.8 eV per anion family. Converting to wavelengths places onsets in the deep UV ( 94 nm; 100 nm; LiFSI 141 nm; NaFSI 148 nm). Results for isolated species or embedded clusters are NISQ‐feasible, with solvent shifts incorporable via classical ‐solvation. Current quantum algorithms capture excitation trends, advancing electrolyte design.
ABSTRACT Accurate prediction of excited states in battery electrolytes is crucial for understanding photostability, oxidative stability, and degradation. We employ hybrid quantum‐classical algorithms–the Variational Quantum Eigensolver (VQE) for ground states and the quantum equation of motion (qEOM) for vertical singlet excitations to study , , LiFSI, and NaFSI. Compact active spaces from frontier orbitals were mapped to qubits and reduced via symmetry tapering and commuting‐group measurements to lower sampling cost. Within 10‐qubit models, VQE‐qEOM agrees closely with exact diagonalization, while sample‐based quantum diagonalization (SQD) in larger spaces recovers near‐exact (subspace‐FCI) energies. Spectra show clear anion‐cation trends within the VQE‐qEOM framework: salts have higher first‐excitation energies ( 13.2 eV) and a compact three‐state cluster at 12–13 eV, whereas FSI salts exhibit lower onsets (8–9 eV) with nearly degenerate and states and a higher separated by 1.3 eV. Independent TDDFT calculations yield systematically lower absolute excitation energies but reproduce the same anion‐ and cation‐dependent trends, confirming that the relative ordering and physical interpretation of the quantum results are robust. Replacing with narrows the gap by 0.4–0.8 eV per anion family. Converting to wavelengths places onsets in the deep UV ( 94 nm; 100 nm; LiFSI 141 nm; NaFSI 148 nm). Results for isolated species or embedded clusters are NISQ‐feasible, with solvent shifts incorporable via classical ‐solvation. Current quantum algorithms capture excitation trends, advancing electrolyte design.
Quantum Simulations of Battery Electrolytes with VQE-qEOM and SQD: Active-Space Design, Dissociation, and Excited States of LiPF6, NaPF6, and FSI Salts
Accurate prediction of excited states in battery electrolytes is central to understanding photostability, oxidative stability, and degradation. We employ hybrid quantum-classical algorithms -- the Variational Quantum Eigensolver (VQE) for ground states combined with the quantum equation of motion (qEOM) for vertical singlet excitations -- to study LiPF6, NaPF6, LiFSI, and NaFSI. Compact active spaces were constructed from frontier orbitals, mapped to qubits, and reduced via symmetry tapering and commuting-group measurements to lower sampling cost. Within $\sim10−qubitmodels,VQE−qEOMagreescloselywithexactdiagonalizationofthesameHamiltonians,whilesample−basedquantumdiagonalization(SQD)inlargeractivespacesrecoversnear−exact(subspace−FCI)energies.Thespectradisplayclearanionandcationtrends:PF_6$ salts exhibit higher first-excitation energies (e.g., LiPF6 $\approx13.2eV)andacompactthree−stateclusterat12−13eV,whereasFSIsaltsshowsubstantiallyloweronsets(\approx8−9eV)withanear−degenerate(S_1,S_2)followedbyS_3$ $\sim1.3eVhigher.SubstitutingLi^+$ with Na+ narrows the gap by $\sim0.4−0.8eVwithineachanionfamily.ConvertingS_1$ to wavelengths places the onsets in the deep-UV (LiPF6 $\sim94nm;NaPF_6$ $\sim$100 nm; LiFSI $\sim$141 nm; NaFSI $\sim$148 nm). All results pertain to isolated species or embedded clusters appropriate to the NISQ regime; solvent shifts can be incorporated a posteriori via classical Δ-solvation or static embedding. These results demonstrate that current quantum algorithms can deliver chemically meaningful excitation and binding trends for realistic electrolyte motifs and provide quantitative baselines to guide electrolyte screening and design.
Accurate prediction of reaction barriers and transition states is central to understanding electrolyte degradation pathways in battery systems, yet existing approaches face significant computational trade-offs. Classical quantum-chemistry methods like density functional theory (DFT) scale favorably but often miss crucial multi-reference character at transition states, while high-accuracy methods such as CCSD(T) become prohibitively expensive for realistic systems. Recent quantum algorithmic approaches, including Variational Quantum Eigensolver (VQE) and Quantum Subspace Diagonalization (QSD), offer pathways toward near-chemical accuracy but suffer from manual active-space selection, excessive measurement overhead, and lack of systematic refinement protocols. We introduce Adaptive Quantum Subspace Diagonalization (A-QSD), a comprehensive pipeline that addresses these limitations through automated chemically-aware active-space selection, compact matrix-element estimation via Hadamard test and classical shadows, and iterative quantum imaginary-time evolution (QITE) preconditioning. Targeting ethylene glycol oxidation pathways relevant to battery electrolyte stability, A-QSD achieves transition-state energy accuracy within 0.1 eV of high-level references while maintaining resource requirements of <=18 qubits and <=700 seconds runtime per reaction point. This work demonstrates the first systematic quantum approach for mapping realistic electrolyte reaction coordinates, establishing a practical framework for quantum-enhanced materials discovery in energy storage 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 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.
Accurately capturing electron correlation in large-scale molecular systems remains one of the foremost challenges in quantum chemistry and a primary driver for the development of quantum algorithms. Classical configuration-interaction methods, while rigorous, suffer from exponential scaling, rendering them impractical for large or strongly correlated systems. Overcoming this limitation is central to realizing the promise of quantum computing in chemistry. Here, we investigate the pyridine-Li ion complex using three quantum algorithms: the variational quantum eigensolver (VQE), the subspace quantum diagonalization (SQD) method, and the recently introduced handover iterative VQE (HI-VQE). Our results demonstrate how new generations of hybrid quantum-classical frameworks overcome the scalability and noise sensitivity that constrain conventional VQE approaches. SQD and HI-VQE achieve ground-state energy calculations for problem sizes inaccessible to classical computation, marking a clear advance toward quantum advantage. In particular, HI-VQE enables calculations within active spaces as large as (24e,22o), requiring 44 qubits-well beyond the reach of classical CASCI and VQE. This capability provides a systematic pathway for incorporating increasing numbers of electrons into quantum treatment, thereby approaching exact molecular energies. Importantly, both SQD and HI-VQE exhibit robustness against hardware noise, a critical improvement over earlier approaches. By enabling quantum simulations of molecular systems previously deemed intractable, SQD and HI-VQE offer a realistic route toward practical quantum advantage in computational chemistry. The comparison between HI-VQE and SQD shows that optimizing circuit parameters is crucial for accurate simulation.
Variational quantum eigensolver (VQE) is a hybrid quantum-classical technique that leverages noisy intermediate scale quantum (NISQ) hardware to obtain the minimum eigenvalue of a model Hamiltonian. VQE has so far been used to simulate condensed matter systems as well as quantum chemistry of small molecules. In this work, we employ VQE methods to obtain the ground-state energy of LiCoO2, a candidate transition metal oxide used for battery cathodes. We simulate Li2Co2O4 and Co2O4 gas-phase models, which represent the lithiated and delithiated states during the discharge and the charge of the Li-ion battery, respectively. Computations are performed using a statevector simulator with a single reference state for three different trial wavefunctions: unitary coupled-cluster singles and doubles (UCCSD), unitary coupled-cluster generalized singles and doubles (UCCGSD) and k-unitary pair coupled-cluster generalized singles and doubles (k-UpCCGSD). The resources in terms of circuit depth, two-qubit entangling gates and wavefunction parameters are analyzed. We find that the k-UpCCGSD with k=5 produces results similar to UCCSD but at a lower cost. Finally, the performance of VQE methods is benchmarked against the classical wavefunction-based methods, such as coupled-cluster singles and doubles (CCSD) and complete active space configuration interaction (CASCI). Our results show that VQE methods quantitatively agree with the results obtained from CCSD. However, the comparison against the CASCI results clearly suggests that advanced trial wavefunctions are likely necessary to capture the multi-reference characteristics as well as the correlations emerging from high-level electronic excitations.
Quantum-chemical simulations are essential for predicting energies of chemical reactions. Accurately solving the many-body Schrödinger equation for reagent and product states of most relevant chemical processes is, however, unfeasible. Quantum computing offers a pathway for predicting energies of correlated electronic systems with localized interactions. Here, we apply a quantum embedding approach for investigating oxygen reduction reactions at the electrode surface in Lithium batteries, a representative example of energetic analysis in localized chemical reactions. We employ an active space selection method based on density difference analysis for identifying the orbitals involved in the reaction. Leveraging the Local Unitary Cluster Jastrow ansatz for state preparation, the active-space orbitals are then processed on a quantum computer. As quantum algorithms, we use Sample-based Quantum Diagonalization, SQD, and its extended version, Ext-SQD, which integrates electronic excitations into the quantum-selected electronic configuration subspace. The largest configurations are represented by quantum circuits mapped onto 80 qubits of an IBM Heron R2 quantum processing unit. For up to 12 orbitals, we are able to benchmark the quantum-computed reaction energies against results obtained with Complete Active Space Configuration Interaction. For benchmarking results in active spaces as large as 32 orbitals, we resort to Heat-Bath Configuration Interaction and Coupled Cluster Singles and Doubles calculations, respectively. At 27 orbitals, the Ext-SQD results exhibit prediction accuracy improvements with regard to the standard, quantum-chemical reference methods that remain computationally feasible at that scale. The results indicate the potential of sample-based quantum diagonalization for performing high-accuracy reaction modeling in chemistry and materials science.