From Paper to Program: Accelerating Quantum Many-Body Algorithm Development via a Multi-Stage LLM-Assisted Workflow

TL;DR

This paper presents a multi-stage LLM-assisted workflow for developing quantum many-body algorithms, externalizing critical computational knowledge to improve reliability and significantly reduce development time.

Contribution

The paper introduces an intermediate technical specification step, externalizing implementation details, which enhances code correctness and accelerates quantum algorithm development.

Findings

Externalized content enables reliable code generation.

Workflow reproduces key physical properties of quantum models.

Development time reduced from weeks to under 24 hours.

Abstract

Large language models (LLMs) can generate code rapidly but remain unreliable for scientific algorithms whose correctness depends on structural assumptions rarely explicit in the source literature. We introduce a multi-stage LLM-assisted workflow that separates theory extraction, formal specification, and code implementation. The key step is an intermediate technical specification -- produced by a dedicated LLM agent and reviewed by the human researcher -- that externalizes implementation-critical computational knowledge absent from the source literature, including explicit index conventions, contraction orderings, and matrix-free operational constraints that avoid explicit storage of large operator matrices. A controlled comparison shows that it is this externalized content, rather than the formal document structure, that enables reliable code generation. As a stringent benchmark, we apply this workflow to the Density-Matrix Renormalization Group (DMRG), a canonical quantum many-body algorithm requiring exact tensor-index logic, gauge consistency, and memory-aware contractions. The resulting code reproduces the critical entanglement scaling of the spin-$1/2$ Heisenberg chain and the symmetry-protected topological order of the spin-$1$ Affleck--Kennedy--Lieb--Tasaki model. Across 16 tested combinations of leading foundation models, all workflows satisfied the same physics-validation criteria, compared to a 46\% success rate for direct, unmediated implementation. The workflow reduced a development cycle typically requiring weeks of graduate-level effort to under 24 hours.