研究者参与循环的进化式发现：LLM 引导程序演化生成纠缠辅助量子码族

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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.

Comments:	25 pages, 6 figures. Code, data and Lean proofs: this https URL
Subjects:	Artificial Intelligence (cs.AI); Information Theory (cs.IT)
MSC classes:	68T20, 68W50, 68T05, 68V15, 81P73
ACM classes:	I.2.2; I.2.8; I.2.6; I.2.3; E.4
Cite as:	arXiv:2610.41183 [cs.AI]
	(or arXiv:2610.41183v1 [cs.AI] for this version)
	https://doi.org/10.48550/arXiv.2610.41183 arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Jae-Hyun Baek [view email]
[v1] Fri, 30 Oct 2026 03:02:10 UTC (191 KB)