# Co-Designing Quantum Codes with Transversal Diagonal Gates via Multi-Agent Systems

arXiv: https://arxiv.org/abs/2510.20728 · HTML: https://mlsanity.com/paper/2510.20728/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 45 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 12 of 12)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Cognitive Architectures for Language Agents](https://mlsanity.com/paper/2309.02427/) (2023)
- [SciCode: A Research Coding Benchmark Curated by Scientists](https://mlsanity.com/paper/2407.13168/) (2024)
- [Can Theoretical Physics Research Benefit from Language Agents?](https://mlsanity.com/paper/2506.06214/) (2025)

## Built on by (most cited first, 4 of 4)

- [Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution](https://mlsanity.com/paper/2606.24808/) (2026)
- [OmniQEC: discovering practical quantum error-correcting codes by an AI scientist](https://mlsanity.com/paper/2607.25865/) (2026)
- [Multi-agent discovery of practical quantum LDPC codes](https://mlsanity.com/paper/2608.08996/) (2026)
- [Symmetry and AI-assisted discovery of magic-state factories](https://mlsanity.com/paper/2610.06535/) (2026)

## Abstract (arXiv)

Exact scientific discovery requires more than heuristic search: candidate constructions must be turned into exact objects and checked independently. We address this gap by extending TeXRA with an independent Lean 4 verification layer, turning it into a human-guided multi-agent platform for exact scientific discovery. The platform couples symbolic synthesis, combinatorial and linear-programming search, exact reconstruction of numerical candidates, and formal verification in Lean. We apply this platform to nonadditive quantum error-correcting codes with prescribed transversal diagonal gates within the subset-sum linear-programming (SSLP) framework. In the distance-2 regime where logical states occupy distinct residue classes, the platform yields a Lean-certified catalogue of 14,116 codes for K∈2,3,4 and up to six physical qubits, realizing cyclic logical orders 2 through 18, from which we extract closed-form infinite families. We also construct a residue-degenerate ((6,4,2)) code implementing the logical controlled-phase gate diag(1,1,1,i). At distance 3, we resolve the transversal-T problem for ((7,2,3)) codes within the complementary binary-dihedral BD16 setting: among the 12 candidates surviving the SSLP filters, 10 admit exact realizations and 2 are excluded by no-go proofs. All accepted constructions, families, and no-go results are formalized and checked in Lean, illustrating how AI-assisted workflows can bridge search, exact reconstruction, and formal proof in the physical sciences.