用大模型引导程序进化,自动发现新型量子纠错码。
Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search
- 大模型变异生成量子码构造代码,结合多阶段验证
- 发现465个新码,包括[[288,16,12]]等高性能非分解码
- 适合量子计算、编码理论研究者,可拓展至其他结构搜索
量子低密度奇偶校验码发现需在庞大的代数设计空间中搜索,并可靠验证候选码的参数与等价类。本文提出一种由大语言模型引导的进化工作流,通过语言模型变异生成双变量自行车码及其扰动变体的代码构想。经过五轮实验,系统执行约1650次进化迭代,筛选约2×10⁵个候选码,耗时约140小时,大模型推理成本约400美元。候选码通过分阶段验证流程评估:包括GF(2)秩计算、距离估计与认证、混合整数线性规划、BLISS Tanner图去重、可分解性分析及局部Clifford等价检查。在码长n≤360时,共发现465个不同候选码:97个CSS双变量自行车码和368个非CSS扰动变体。CSS搜索复现了已知高性能码,并发现新的有限长度代表码,包括不可分解的[[288,16,12]]码,以及距离d=8、信息位k=50的高权重码。非CSS搜索获得与[[144,12,12]]同等级别的粗码性能指标,并报告多个高距离候选码的认证值或上界(基于MILP状态)。结果表明,大模型引导的程序演化可作为结构化量子码发现的实用工具,前提是配合独立验证。
原文摘要 · Abstract (English)
Quantum LDPC code discovery requires searching large algebraic design spaces while reliably certifying the parameters and equivalence classes of any candidates found. We introduce an LLM-guided evolutionary workflow in which language models mutate Python programs that generate bivariate-bicycle and perturbed bivariate-bicycle code ansätze. Across five campaigns, the system performed approximately 1{,}650 evolutionary iterations, screened about $2 \times 10^5$ candidate codes, and required ${\sim}140$ hours of computation and ${\sim}$US\$400 in LLM inference cost. Candidate codes are evaluated through a staged validation pipeline combining $\mathrm{GF}(2)$ rank computation, distance estimation and certification, mixed-integer linear programming, BLISS Tanner-graph deduplication, decomposability analysis, and local-Clifford equivalence checks. At block length $n \leq 360$, the workflow identifies 465 distinct candidate codes: 97 CSS bivariate-bicycle codes and 368 non-CSS perturbed variants. The CSS search recovers known high-performing codes and finds new finite-length representatives, including an indecomposable [[288,16,12]] code and higher-weight codes with up to $k = 50$ at distance $d = 8$. The non-CSS search produces perturbed codes matching the gross-code figure of merit at [[144,12,12]], along with additional high-distance candidates reported as certified values or upper bounds according to MILP status. Overall, these results show that LLM-guided program evolution can serve as a practical tool for structured quantum-code discovery when paired with independent evaluation.
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