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.
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.
We present a comprehensive theoretical analysis of quantum subspace diagonalization methods for molecular electronic structure calculations, establishing rigorous complexity bounds and convergence guarantees. Building on recent developments in adaptive quantum algorithms for chemical systems, we formulate a general mathematical framework that describes how quantum computers can efficiently explore molecular potential energy surfaces through iterative subspace construction. Our theory characterizes the relationship between subspace dimension, basis set selection, and solution accuracy for ground and excited state calculations. We derive analytical expressions for the number of quantum measurements required to achieve chemical accuracy and establish conditions under which quantum subspace methods offer polynomial advantages over classical approaches. The framework incorporates realistic noise models, providing performance predictions for near-term quantum devices. We analyze trade-offs between circuit depth, measurement overhead, and solution quality, identifying optimal operating regimes for different molecular systems. Special attention is devoted to transition-state mapping for chemical reactions, where we prove that adaptive subspace selection achieves exponential reduction in required measurements compared to uniform sampling. Applications to battery electrolyte reactions, drug discovery, and materials design demonstrate the practical utility of our theoretical predictions. This work establishes quantum subspace methods as a rigorous alternative to variational approaches, offering theoretical guarantees absent in parameter-optimization-based algorithms while maintaining compatibility with near-term quantum hardware constraints.
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.
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.
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 and hybrid quantum-classical algorithms have the potential to improve the accuracy and scale of quantum chemistry and impact a broad range of applications such as drug discovery and catalysis. In particular, subspace methods such as sample-based quantum diagonalization (SQD) can already tackle classically challenging systems. However, practical algorithms that go beyond the computation of electronic ground and excited states are still scarce. Here, we introduce the variable-geometry sample-based quantum diagonalization (VGSQD) algorithm, which extends SQD to variable molecular geometries by reusing quantum samples from a reference geometry at displaced ones, thus significantly reducing quantum computational cost. Using circuits of up to 124 qubits on ibm-quebec, an IBM Heron r2 quantum processor, we determine the equilibrium geometry and energy of the weakly bound, strongly correlated beryllium dimer, as well as the water molecule. Finally, we extend VGSQD to chemical reactions and compute the minimum energy path and energy barrier of a hydrogen exchange reaction. The results are comparable with state-of-the-art classical methods such as CCSD(T) and DMRG. This work broadens the scope of quantum algorithms for chemistry, from energies to geometry optimization and reaction pathways, both essential for practical applications.
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.