发表机构
Graduate School of Mathematics, Nagoya University（名古屋大学大学院理学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于稀疏李括号数据和已知谱隙的量子算法，用于构造李代数根基的近似系数空间投影算子，可检验紧量子动力学中中心是否平凡，为内部守恒方向提供可控检验。
AI 中文摘要
每个有限维实或复李代数都具有最大可解理想，即其根基。在闭合量子系统的紧动力学李代数（DLA）中，该根基为中心；向其投影可分离出与给定代数可交换的方向。基于稀疏李括号数据和已知谱隙，我们构造了一个量子电路，该电路可近似编码此系数空间投影算子。一般构造结合了导出代数映射与基灵型，而紧性使得仅基灵型即可满足要求，这一区别对数值敏感性至关重要，我们的主定理在适配中心与半单部分的不变标准正交基下给出了其精确规律。在具有非零半单部分的紧实代数中，一般算子的条件数为该部分基灵型条件数的二分之三次方。只要任意非零中心具有至少规定的最小维数，紧投影算子即可对中心是否平凡产生有界误差的检验，这为紧量子动力学中的内部守恒方向提供了可控检验方法。
英文摘要
Every finite-dimensional real or complex Lie algebra has a largest solvable ideal, its radical. In the compact dynamical Lie algebra (DLA) of a closed quantum system, this radical is the center; projecting onto it isolates directions that commute with the supplied algebra. With sparse Lie-bracket data and a known spectral gap, we construct a quantum circuit that approximately encodes this coefficient-space projector. The general construction combines the derived-algebra map with the Killing form, whereas compactness makes the Killing form alone sufficient. This distinction matters for numerical sensitivity, and our main theorem gives its exact law under an invariant-orthonormal basis adapted to the center and semisimple part. In a compact real algebra with a nonzero semisimple part, the condition number of the general operator is the three-halves power of the Killing-form condition number on that part. The compact projector in turn yields a bounded-error test for whether the center is trivial, provided that any nonzero center has at least a stated minimum dimension. This gives a controlled test for internal conserved directions in compact quantum dynamics.
