AI 中文总结
研究针对未知酉算子的谱分解，开发了量子位原生的雅可比对角化算法的量子实现，避免算子显式重构等，通过量子变分优化实现吉文斯旋转，经数值模拟验证算法性能，搭建起经典与量子迭代矩阵算法间的桥梁。
AI 中文摘要
雅可比对角化是一种用于厄米矩阵以及更一般的正规矩阵谱分解的长期存在的数值算法。在这项工作中，我们为未知酉算子开发了一种量子位原生的雅可比对角化算法的量子实现。所提出的框架避免了算子的显式重构和受控酉操作。每个基本的双参数吉文斯旋转通过两个连续的单参数量子变分优化来实现，这在实验上是直接可访问的。还引入了一种干涉测量协议来提取对角化酉矩阵的本征值，直至一个全局相位。对哈尔随机酉矩阵集合的数值模拟表明，所提出的算法保留了经典雅可比方法的特征收敛行为，并且在基本操作数量上与维度\(d\)呈现预期的二次缩放，与经典对应方法相当。这些结果将所提出的算法确立为一种自然适用于量子位架构的结构化量子数值线性代数算法，并在经典迭代矩阵算法及其量子实现之间架起了一座桥梁。
英文摘要
Jacobi diagonalization is a long-established numerical algorithm for the spectral decomposition of Hermitian and, more generally, normal matrices. In this work, we develop a qudit-native quantum realization of the Jacobi diagonalization algorithm for unknown unitary operators. The proposed framework avoids explicit reconstruction of the operator and controlled-unitary operations. Each elementary two-parameter Givens rotation is implemented through two sequential single-parameter quantum variational optimizations that are directly accessible experimentally. An interferometric protocol is further introduced for extracting the eigenvalues of the diagonalized unitary, up to an overall global phase. Numerical simulations on ensembles of Haar-random unitary matrices demonstrate that the proposed algorithm preserves the characteristic convergence behavior of the classical Jacobi method and exhibits the expected quadratic scaling in the number of elementary operations with the dimension $d$, comparable to its classical counterpart. The results establish the proposed algorithm as a structured quantum numerical linear algebra algorithm naturally suited to qudit architectures and provide a bridge between classical iterative matrix algorithms and their quantum realizations.
Comments14 pages, 3 figures
