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Accuracy And Resource Requirements for Quantum Impurity Solvers in Correlated Cathode Materials: An Exact-DMRG Benchmark

Tridip Das, Maurice Benson, Daniel Takahashi

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.2139/ssrn.7631578

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Quantum impurity solvers are the computational bottleneck of quantum embedding approaches to correlated materials, such as dynamical mean-field theory (DMFT). We show that neural networks trained on synthetic, material-agnostic data learn the impurity mapping from hybridization functions and local interactions to Green's functions with quantitative accuracy for both model systems and real materials, providing fast solvers for single- and multi-orbital models. Benchmarks against numerically controlled quantum Monte Carlo show that the method reproduces the Mott transition, multi-orbital phase diagrams of Hubbard-Kanamori models, and the electronic properties of SrVO3_33​ and SrMnO3_33​. The learned solvers achieve orders-of-magnitude speedup and can initialize controlled calculations, dramatically accelerating DMFT while preserving accuracy.
We develop an end-to-end framework for assessing a quantum-computing application in industrial materials science: the screening of strongly correlated oxygen-electrode materials for SOFCs and SOECs. We formulate the materials problem in terms of interface observables including oxygen-vacancy formation energies, vacancy migration barriers, and electronic conductivity. We describe how these observables can be obtained using a diagrammatic GW-based embedding, either GW+DMFT or self-energy embedding theory (SEET), applied to a DFT-screened shortlist. The atomistic electrode/electrolyte interface defines the electronic structure problem from which the correlated impurity models are constructed. Quantum impurity solvers would provide the finite-temperature impurity Green's functions required by the embedding. The computational challenges that classical solvers may encounter as the interacting active space grows, together with the polynomial scaling of quantum Hamiltonian simulation for efficiently represented discretized models, open an opportunity for quantum advantage. We identify the benchmarks needed to assess this opportunity through convergence of vacancy and migration energetics and comparison with the best applicable classical solvers. We provide illustrative logical qubit counts and identify the thermal state preparation, simulation, measurement, and repeated-solve costs needed for a complete resource assessment. We connect microscopic observables to macroscopic engineering metrics using a continuum model for mixed ionic--electronic conducting oxygen electrodes that couples oxygen surface exchange, solid-state oxygen transport, electrode microstructure, and finite electrode thickness. Finally, we estimate the potential worldwide business value of improved electrode materials under SOFC and SOEC deployment scenarios informed by public technical targets and electrolyser deployment data.