Quantum Singular Value Decomposition of Spin Correlation Matrix in One-Dimensional Heisenberg Model

二维二聚化量子Heisenberg模型的拓扑序与退化奇异值谱

Topological Order and Degenerate Singular Value Spectrum in Two-Dimensional Dimerized Quantum Heisenberg Model

通过显式求解二维二聚量子海森堡模型的张量积态近似，研究了奇异值谱简并度与拓扑序之间的关系.基于基态解，我们发现在阻挫区存在非零的拓扑纠缠熵。它表示可能的拓扑相位。此外，我们发现张量积态中每个链的奇异值谱仅在这一阶段是双简并的。退化的奇异值谱是强大的对各种类型的扰动，按照我们的期望拓扑秩序。我们的结果支持了拓扑序、长程纠缠和主退化奇异值之间的联系。在张量积态近似下，奇异值谱的数值计算比拓扑纠缠熵的数值计算要少得多。我们的结果提供了一个更可行的方法来确定一般的挫折系统的拓扑顺序。

基于量子退火的奇异值分解

Singular-value decomposition using quantum annealing

在本研究中，我们演示了如何执行，使用量子退火，奇异值分解和主成分分析。量子退火提供了一种找到系统基态的方法，而奇异值分解需要最大本征态。其核心思想是对最终哈密顿量进行符号变换，并通过量子退火得到最大本征态。此外，绝热时间尺度是通过对最大本征值的近似得到的。

由外尔-海森堡串生成的多量子三态门的分解

Decomposition of multi-qutrit gates generated by Weyl-Heisenberg strings

本文针对量子三态系统，开发将外尔-海森堡算子张量积指数分解的算法，并扩展到盖尔曼串生成的酉运算，用于分解多量子三态门，应用于图k着色问题的量子近似优化算法，还解决了路由挑战。

Phase Factors in Singular Value Decomposition and Schmidt Decomposition

In singular value decomposition (SVD) of a complex matrix A, the singular vectors or the eigenvectors of AA† and A†A are unique up to complex phase factors. Thus, the two unitary matrices in SVD are unique up to diagonal matrices of phase factors, the phase-factor matrices. Also, the product of these two phase-factor matrices, or the product of phase factors of the corresponding singular vectors with the same singular value, is unique. In the Schmidt decomposition, a phase-factor matrix is a phase rotation operator acting on a subsystem alone. We summarize here three simple steps to consistent…

Quantum Higher Order Singular Value Decomposition

Higher order singular value decomposition (HOSVD) is an important tool for analyzing big data in multilinear algebra and machine learning. In this paper, we present two quantum algorithms for HOSVD. Our methods allow one to decompose a tensor into a core tensor containing tensor singular values and some unitary matrices by quantum computers. Compared to the classical HOSVD algorithm, our quantum algorithms provide an exponential speedup. Furthermore, we introduce a hybrid quantum-classical algorithm of HOSVD model applied in recommendation systems.

Variational Quantum Singular Value Decomposition

Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantu…