llm-structured-concept-evolution

name	llm-structured-concept-evolution
description	Structured Concept Evolution (SCE) — search framework pairing LLMs with structured algebraic mutation grammars to discover quantum LDPC code families. Evolves structured concepts (algebraic specifications + executable programs) via hierarchical mutations on group algebra, protograph geometry, or base space, discovering competitive CSS qLDPC codes including non-abelian group constructions beyond bivariate-bicycle codes. Use when discovering quantum error-correcting codes, running LLM-guided algebraic search, or exploring lifted-product code families.
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2606.24808","published":"2026-06-23","authors":"Zidu Liu, Florian Marquardt","tags":["quantum","error-correction","llm","ldpc","structured-concept-evolution","css-codes","non-abelian"]}

LLM Structured Concept Evolution for Quantum LDPC Code Discovery

Paper Summary

Title: Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution arXiv: 2606.24808 Date: June 23, 2026 Authors: Zidu Liu, Florian Marquardt

Core Innovation

Structured Concept Evolution (SCE) is a search framework that pairs a large language model with a structured algebraic mutation grammar to discover lifted-product code families — a class of CSS qLDPC (quantum low-density parity-check) codes. Unlike prior approaches that ask LLMs to design codes from first principles, SCE consisting of: