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

Abstract

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/linear-combination-of-unitaries (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, 𝜆 rs)} = (pq|rs), (ii) truncates the factorization at rank r and reports reconstruction residuals, (iii) evaluates DF resource proxies via 𝜆^DF _LCU and𝜆^DF_Burg, 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 ^corr_ads . 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.

Received: 12 January 2026 | Revised: 14 May 2026 | Accepted: 28 May 2026

Conflicts of Interest

The author declares that he has no conflicts of interest to this work.

Data Availability Statement

Data are available from the corresponding author upon reasonable request.

Author Contribution Statement

Miguel Angel Vargas Cruz: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Writing - review & editing, Visualization, Supervision, Project administration.