Quantifying the Coherence Wall: FeMoCo Quantum Chemistry from 48 to 108 Qubits on IBM Heron r2

We quantify the depth-dependent loss of many-body correlation information in FeMoCo-scale quantum chemistry circuits executed on IBM Heron r2. The workflow combines LUCJ circuit execution, Aurora-DD control, sample-based quantum diagonalization (SQD), DMRG prior construction, and ph-AFQMC refinement across 48-, 56-, 80-, and 108-qubit active-space instances. Rather than treating the 108-qubit energy as a chemical-accuracy claim, we separate statistical precision, systematic phaseless bias, and extractable correlation signal. The 108-qubit CAS(54e,54o) run reaches a ph-AFQMC statistical standard error of ±0.67 mHa, while the single-determinant phaseless bias remains approximately 1,103 mHa relative to DMRG M = 500. Conversely, a classical DMRG multi-determinant ph-AFQMC route reaches chemical accuracy at 48 qubits, with a residual phaseless bias of +1.07 mHa. Four-point spatial-correlation amplitudes decay from 0.226 at 48 qubits to 0.101 at 80 qubits and 0.045 at 108 qubits; fitting the 48-qubit amplitude gives a per-qubit scaling parameter ϵq = 0.0304 that predicts the 80- and 108-qubit amplitudes within 19–26% relative error without additional free parameters. Exhaustive Bayesian and machine-learning signal extraction yields an out-of-fold ceiling of r ≈ 0.03 at 108 qubits under the present Heron r2, shot-count, circuit-depth, and DMRG M = 800 reference conditions. We therefore define the observed coherence wall as a conditional hardware-characterization metric for this benchmark rather than a universal physical constant. The results suggest that residual incoherent noise channels, including TLS-associated loss and relaxation, now dominate over statistical sampling error in this regime.