发表机构
Leibniz Universität Hannover; Tata Institute of Fundamental Research; Unitary Foundation（汉诺威莱布尼茨大学; 塔塔基础研究所; 幺正基金会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
PauLie是基于反交换图归约的开源框架，可快速判定任意泡利字符串生成的DLA的同构类型，运行时间复杂度低，可用于量子系统相关的多种任务。
AI 中文摘要
动力学李代数（DLA）决定了量子系统的可控性、表达能力和模拟复杂度，显式计算它一直是主要的计算瓶颈：暴力李闭包的规模随量子比特数n呈指数增长。然而许多应用仅需参考DLA的同构类型。我们引入PauLie，这是一个开源框架，基于Aguilar等人的反交换图归约，可对任意泡利字符串生成的DLA判定其同构类型。PauLie的运行时间为O(n|𝒢|max(n,|𝒢|))，其中|𝒢|是生成元的数量，将DLA分类转化为常规预处理步骤。我们展示了它在李代数模拟路由、Cartan分解的结构预言、变分量子算法的贫瘠平台诊断以及生成具有最优生成率的通用泡利字符串生成元集方面的应用。
英文摘要
The dynamical Lie algebra (DLA) governs the controllability, expressibility, and simulation complexity of a quantum system. Explicitly computing it has been a major computational bottleneck: brute-force Lie closure scales exponentially in the number of qubits $n$. Many applications, however, consult only the isomorphism type of the DLA. We introduce PauLie, an open-source framework that decides this isomorphism type for DLAs generated by arbitrary Pauli strings, building on the anticommutation-graph reduction of Aguilar et al. PauLie runs in $O(n|\mathcal{G}|\max(n,|\mathcal{G}|))$ time, where $|\mathcal{G}|$ is the number of generators, turning DLA classification into a routine preprocessing step. We demonstrate its use as a structural oracle for routing Lie-algebraic simulation and Cartan decomposition, diagnosing barren plateaus in variational quantum algorithms, and engineering universal Pauli string generator sets with optimal generation rate.
CommentsAccepted at the 2026 IEEE International Conference on Quantum Computing and Engineering (QCE)
