Researcher-in-the-Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families
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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 q3 at n2q+1 and for q=2 at odd n5. 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.
Autores
Jae-Hyun Baek, Byung-Sun Won, Jon-Lark Kim
Categorías
overfeed.news indexa y enlaza. Publicamos un extracto breve; el artículo completo sigue en arXiv AI Papers.
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