Researcher-in-the-Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families
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≥3 at n≥2q+1 and for q=2 at odd n≥5. 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.
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BibTeX
@misc{baek2026researcherintheloop,
title = {{Researcher-in-the-Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families}},
author = {Jae-Hyun Baek and Byung-Sun Won and Jon-Lark Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41183},
eprint = {2610.41183},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41183},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Researcher-in-the-Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families
AU - Jae-Hyun Baek
AU - Byung-Sun Won
AU - Jon-Lark Kim
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41183
UR - https://arxiv.org/abs/2610.41183
AB - 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≥3 at n≥2q+1 and for q=2 at odd n≥5. 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.
ER -