Modeling approaches to support discovery of quantum properties of materials with validation by graphene studies

Abstract

Quantum subspace diagonalization (QSD) is a near-term strategy for electronic-structure problems that avoids the deep, heavily optimized circuits of the variational quantum eigensolver by preparing a small basis, measuring a subspace Hamiltonian on hardware, and diagonalizing it classically. We benchmark two QSD variants, a seniority-based orthogonal method (Q-SENSE) and a non-orthogonal correlated-basis method (CVQE), on a minimal two-site Hubbard model whose parameters correspond to a graphene (symmetric) and a hexagonal boron nitride-like (sublattice-broken) sublattice motif. Because the model is exactly solvable, hardware results are graded against the true ground state and against a Hartree-Fock mean-field baseline, isolating the correlation energy each method recovers. On IBM Heron superconducting processors we find that the symmetric case recovers essentially all of the correlation energy with inexpensive readout-error mitigation, whereas the gapped case is limited by two-qubit gate error on the hopping terms. On a single device (ibm_kingston), readout mitigation alone recovers 75% of the hBN correlation energy; adding zero-noise extrapolation reduces the per-run error and raises the mean recovery to 98% ± 18% (n=5), though the run-to-run variance remains large relative to the mean.