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

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 [Fe₄S₄(SCH₃)₄]²⁻ cubane (54 electrons, 36 orbitals, 72 data qubits; 88 total qubits), this lowers the mean-field reference by ≈ 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 × 10¹⁰, we reach $E = -327.235076$ Ha. This is 4.3 mHa above the finite-$D = 4000$ DMRG value (-327.2393952 Ha) and ~ 512-517 mHa below a previous same-active-space RHF-reference SQD calculation. Extrapolating to the d → ∞ limit via a Gaussian-in-log d fitting ansatz gives an asymptotic estimate E_∞ = -327.244468 Ha ± 1.05 mHa, just 0.33 mHa above our discarded-weight-extrapolated DMRG estimate (ED→∞ = -327.244797 Ha ± 0.46 mHa), well within their combined $1σ$ uncertainty. We characterize the determinant-subspace composition driving convergence, show matching validation on [Fe₂S₂(SCH₃)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.