LLM 程序进化+人工把关发现量子纠错码新族
Researcher-in-the-Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families
LLM 自动写程序进化出量子纠错码，再用 Lean 证明推广成定理，一口气填补 54 个编码表空缺，AI 做数学的新范式。
一个研究者参与闭环的发现流程结合程序进化、精确评估、数学推广与 Lean 形式化证明检查，应用于纠缠辅助量子纠错码（EAQECC）。进化出的程序产生有限比特构造，研究者将其推广为族 [[n,1,n-1;n-q-1]]_q（素数幂 q≥3 且 n≥2q+1，及 q=2 时奇数 n≥5），填补 EAQECC 档案表中 54 个空缺。发布证据包括 115 条已验证码记录、10 个带 DRAT 证明校验的不存在性结果。在 8 组对照实验中，验证选择的迭代程序在未见长度 n=13,15 的执行成功率达 46.1% 和 31.6%，独立生成程序仅为 19.5% 和 3.1%。
Researcher-in-the-Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families
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.
