大语言模型通过结构化概念演化发现量子 LDPC 码
Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution
AI 导读
一项研究提出结构化概念演化方法，让大语言模型通过修改有限群、原型图形状或元素赋值规则来演化量子 LDPC 码构造程序。该方法在数据量子比特少于 600、校验权重不超过 12 的搜索范围内，在部分参数区间超越了已发表的 lifted-product 基准，领先结果均附带精确认证码距。相同演化框架与步数预算下，最佳 LLM 在两个目标上均胜过随机变异和爬山法。
正文 · 原文
Abstract:Quantum low-density parity-check codes promise low-overhead error correction, but high-performing constructions remain hard to find. Here we introduce structured concept evolution, in which a large language model (LLM) evolves construction programs and their internal search strategies by modifying the finite group, protograph shapes or entry-assignment rule. We search for codes with fewer than $600$ data qubits and check weight at most $12$, optimizing $kd^2/n$ or the circuit-level logical error rate. Our method improves on published lifted-product benchmarks in selected parameter regimes, with exactly certified distances for the leading results. Circuit-level optimization typically yields lower logical error rates than $kd^2/n$ optimization, often despite smaller code distances. With the same evolution framework and step budget, the best LLM outperforms all random-mutation and hill-climbing runs on both objectives. Our results point to LLM-driven program search as an approach to designing general quantum LDPC codes.
| Comments: | 23 pages, 4 figures |
| Subjects: | Quantum Physics (quant-ph); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2606.24808 [quant-ph] |
| (or arXiv:2606.24808v2 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2606.24808 arXiv-issued DOI via DataCite |
Submission history
From: Zidu Liu [view email]
[v1]
Tue, 23 Jun 2026 16:56:24 UTC (1,700 KB)
[v2]
Wed, 4 Nov 2026 12:37:38 UTC (260 KB)
来源：arXiv cs.AI · arxiv.org