From Paper to Program: Specification-Guided Implementation of Quantum Many-Body Algorithms with Large Language Model

Turning scientific papers into reliable code requires making implicit computational knowledge explicit. We introduce and evaluate a human-supervised workflow in which large language models develop and review technical specifications before implementing quantum many-body algorithms. The specifications encode conventions, procedures, scaling requirements, and validation gates for mathematical consistency, physical accuracy, and production-scale performance. For the density-matrix renormalization group, all 16 tested specification--implementation model pairings succeed, compared with 6 of 13 direct attempts; two further attempts succeed with a prose specification. For Pfaffian conversion of Hartree--Fock--Bogoliubov states to matrix product states, on eleven matched model--harness configurations, four self-paired workflow attempts pass and no direct attempts do; across all phases, 11 of 26 workflow attempts pass the audit and validation criteria. Cross-model transfer is asymmetric: one implementation model succeeds with all four specifications written by other models, whereas all four reverse-direction attempts fail. A consolidated specification informed by these experiments supports successful implementations in three previously unsuccessful model--harness configurations. Technical specifications therefore guide scalable implementation and help distinguish paper-to-code ambiguity from limitations in implementation capability. We synthesize these findings into the Paper-to-Program Many-Body protocol, which turns implementation experience into reusable review criteria, validation gates, and reporting practices. Publicly archived prompts, transcripts, specifications, code, and validation records support independent verification and extension to other many-body algorithms.