A Discrete Recovery Failure Mode in Sample-Based Quantum Diagonalization Carries Chemically Predictive Information

Sample-based quantum diagonalization (SQD) recovers a molecular ground state from noisy quantum-hardware samples by iteratively selecting a subspace of Slater determinants and diagonalizing the Hamiltonian within it. We show that this recovery process can become trapped in a reproducible "wrong attractor": independent low-shot trials converge to a bit-identical, incorrect fixed point. Escape from this state is discrete rather than continuous — injecting a single missing configuration into the raw sample set restores the correct answer, while further copies of that configuration produce no additional change. We trace this behavior to the internal configuration-recovery iteration on real IBM hardware and confirm it via a controlled injection experiment (5/5 independent reproduction). The same signature generalizes across four chemically distinct molecules spanning a 20-fold range of static-correlation strength (N2, O3, p-benzoquinone, and naphthoquinone), though the magnitude of the recovery does not scale monotonically with correlation strength. This failure mode — not merely its correction — is the central result of this paper. We then ask whether the configuration responsible for escape is chemically arbitrary or chemically meaningful, and find the latter: the second-largest term in the exact configuration-interaction expansion of the neutral molecule provides a predictive indicator of the molecular orbital that becomes occupied upon one-electron reduction, in advance of ever computing the reduced species. This indicator held in 21 blind tests across six molecular classes (quinones, nitroaromatics, an amide, a cyanocarbon acceptor, small inorganics, an extended π-system, and a transition-metal model). A calibrated confidence flag (escape-configuration weight ≥ 1.5%) identified which predictions to trust: every prediction it flagged as high-confidence was correct, though — as with any threshold — some correct predictions fell below it and were (conservatively) flagged as low-confidence instead. We identify and directly verify, via atomic-orbital decomposition, a boundary condition under which the indicator fails: aliphatic carbon–halogen bonds introduce a competing in-plane σ*(C–X) orbital that aromatic carbon–halogen bonds do not, because the halogen lone pair conjugates into the ring π-system in the latter case. We treat this second part of the paper as a derived, still-developing application of the failure mode rather than an established rule, and report its limitations candidly — including a retracted regioselectivity claim whose reversal under a larger basis set directly motivated the confidence threshold used throughout.