Adsorption-Calibrated Double Factorization with λ-Metrics for Qubitization-Oriented Hamiltonians

Low-rank factorizations of the two-electron repulsion integral (ERI) tensor are central to reducing fault-tolerant costs of Hamiltonian simulation in quantum chemistry, particularly under qubitization/LCU constructions where both the block-encoding normalization constant λ and the complexity of Prepare/Select depend on the chosen decomposition. We present a CPU-only, FCIDUMP-first workflow that (i) constructs a spectral double factorization (DF) of the ERI supermatrix G_(pq,rs) = (pq|rs), (ii) truncates the factorization at rank r and reports reconstruction residuals, (iii) evaluates DF resource proxies via λ_LCU^DF and λ_Burg^DF, and (iv) selects an operational rank by enforcing an observable-level constraint on a differential quantity: the MP2 correlation contribution to a model adsorption energy, ΔE_ads,corr. Using NH3 as a minimal Lewis-basic site and CO2 as adsorbate in STO-3G, we sweep intermolecular separations d_N···C ∈ {2.2, 2.6, 3.0} Å and determine the worst-case feasible rank r_worst as the smallest rank satisfying a predefined adsorption-error tolerance across the geometry set. In this toy benchmark, λ-metrics for the complex saturate at moderate ranks while the differential adsorption observable remains sensitive to intermediate-rank components, demonstrating that λ convergence alone can be insufficient for rank selection when targeting chemically relevant differences. The resulting protocol provides a reproducible bridge between DF-based resource estimation and observable-constrained truncation criteria for qubitization-oriented Hamiltonians.