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This paper uses LLM-guided program evolution to find finite quantum error-correcting code constructions, then has researchers generalize them into a family with a Lean-checked algebraic certificate, DRAT-checked nonexistence proofs, and 54 closed gaps in archived tables. The verifiable artifacts are the main contribution, since they make the claims checkable rather than dependent on the search process. The held-out comparison (validation-selected iterative programs vs. independent generation) is informative but rests on only eight paired blocks, and the human researcher's role is substantial, so the result is best read as a demonstration of a workflow rather than evidence of autonomous discovery.
Researcher-in-the-Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families
arXiv:2610.41183v1 Announce Type: new Abstract: LLM-guided program evolution can produce mathematical constructions, but validity, generality, and reproducibility require distinct evidence. We develop a researcher-in-the-loop discovery pipeline that combines program evolution, exact evaluation, mathematical generalization, certified nonexistence checks, and formal proof checking. We apply it to entanglement-assisted quantum error-correcting codes (EAQECCs). Starting from tasks that did not specify a family formula, evolved programs produced finite qubit constructions whose structure researchers generalized to the family $[[n,1,n-1;n-q-1]]_q$ for prime powers $q\ge3$ at $n\ge2q+1$ and for $q=2$ at odd $n\ge5$. Lean checks the algebraic certificate underlying this family. Together with entanglement lifting, the family closes 54 gaps in archived EAQECC tables. The released evidence includes 115 verified code records, ten nonexistence results with checked DRAT proofs, family implementations, and preserved search programs for exact checks and seeded replay. In a controlled cohort of eight paired generation blocks, validation-selected iterative programs achieve success in 46.1% and 31.6% of held-out executions at unseen lengths $n=13,15$, compared with 19.5% and 3.1% for independently generated programs. In this setting, program evolution and researcher analysis turn finite computational discoveries into a proved family with independently checkable evidence.
Abstract:LLM-guided program evolution can produce mathematical constructions, but validity, generality, and reproducibility require distinct evidence. We develop a researcher-in-the-loop discovery pipeline that combines program evolution, exact evaluation, mathematical generalization, certified nonexistence checks, and formal proof checking. We apply it to entanglement-assisted quantum error-correcting codes (EAQECCs). Starting from tasks that did not specify a family formula, evolved programs produced finite qubit constructions whose structure researchers generalized to the family $[[n,1,n-1;n-q-1]]_q$ for prime powers $q\ge3$ at $n\ge2q+1$ and for $q=2$ at odd $n\ge5$. Lean checks the algebraic certificate underlying this family. Together with entanglement lifting, the family closes 54 gaps in archived EAQECC tables. The released evidence includes 115 verified code records, ten nonexistence results with checked DRAT proofs, family implementations, and preserved search programs for exact checks and seeded replay. In a controlled cohort of eight paired generation blocks, validation-selected iterative programs achieve success in 46.1% and 31.6% of held-out executions at unseen lengths $n=13,15$, compared with 19.5% and 3.1% for independently generated programs. In this setting, program evolution and researcher analysis turn finite computational discoveries into a proved family with independently checkable evidence.
25 pages, 6 figures. Code, data and Lean proofs: this https URL
Artificial Intelligence (cs.AI); Information Theory (cs.IT)
I.2.2; I.2.8; I.2.6; I.2.3; E.4
arXiv:2610.41183 [cs.AI]
(or arXiv:2610.41183v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.41183 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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