Broken-Symmetry Reference States for Sample-Based Quantum Diagonalization with Near-DMRG Accuracy

Abstract

Sample-based quantum diagonalization (SQD) accuracy remains limited for strongly correlated systems like iron-sulfur clusters. This accuracy heavily depends on the mean-field reference state, which determines the sampling ansatz and configuration-recovery target. We extend the qcsc-prefect workflow to support a broken-symmetry unrestricted Hartree-Fock (BS-UHF) starting point, derived from atom-localized antiferromagnetic initial guesses. For the $[Fe_4S_4(SCH_3)_4]^{2-}$ cubane (54 electrons, 36 orbitals, 72 data qubits; 88 total qubits), this lowers the mean-field reference by $\approx 534$ mHa relative to the Restricted Hartree-Fock (RHF) solution (-327.0809 vs. -326.5474 Ha). Combined with deep multi-step configuration recovery on ROQUO GPU nodes at subspace dimension $d = 3 \times 10^{10}$, we reach $E = -327.235076$ Ha. This is 4.3 mHa above the finite-$D = 4000$ DMRG value (-327.2393952 Ha) and $\sim 512-517$ mHa below a previous same-active-space RHF-reference SQD calculation. Extrapolating to the $d \to \infty$ limit via a Gaussian-in-log $d$ fitting ansatz gives an asymptotic estimate $E_\infty = -327.244468$ Ha $\pm 1.05$ mHa, just 0.33 mHa above our discarded-weight-extrapolated DMRG estimate ($E_{D\to\infty} = -327.244797$ Ha $\pm 0.46$ mHa), well within their combined $1σ$ uncertainty. We characterize the determinant-subspace composition driving convergence, show matching validation on $[Fe_2S_2(SCH_3)_4]^{2-}$, and report multi-HPC execution on Fugaku, Miyabi-G, and ROQUO. We conclude that reference-state preparation, rather than subspace size alone, is a key driver of SQD energy accuracy under strong electronic correlation.