quant-phJul 8, 2026

Multi-agent Autoformalization of Tensor Network Theory

Authors: Sirui LuErickson TjoaJ. Ignacio Cirac

Organizations: Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany · Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 Munich, Germany

Abstract

We build a team of specialized large language-model agents and present an agent-driven workflow for research-level formalization in theoretical physics, with the autoformalization of the fundamental theorem of matrix-product states as a demonstration. The agents, coordinated through a structured mathematical blueprint and periodic human review, orchestrated and executed the full formalization autonomously. For some statements, the agents were able to explore new proof routes that are not part of the standard literature. Along the way the agents produced extensive tensor-network and quantum-information libraries not previously available in Mathlib, Lean's mathematical library. As a physical application, the formalization also extends towards symmetry-protected topological phases in one dimension. We find that the main bottleneck in large-scale autoformalization is enforcing mathematical intent and we provide a detailed study of the full process and various subtleties involved. We release the codebase as the library \href{https://github.com/LionSR/TNLean}{TNLean}, together with a \nChapters{}-chapter \href{https://lionsr.github.io/TNLean/blueprint/}{blueprint} of the formalization effort.

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