量子极分解算法
Quantum polar decomposition algorithm
摘要：
矩阵$A$的极分解是$A=UB$，其中$B$是正厄米矩阵，$U$是酉矩阵（或者，如果$A$不是正方形，则是等距矩阵）。本文表明，应用哈密顿量$\pmatrix{ 0 & A^\dagger \cr A & 0 \cr} $的能力转化为以确定性方式执行转换$e^{-iBt}$和$U$的能力。我们展示了如何使用量子极分解算法来解决量子Procrustes问题，执行相当好的测量，找到最接近任何哈密顿的正哈密顿，并执行量子奇异值变换的哈密顿版本。
英文摘要：
The polar decomposition for a matrix $A$ is $A=UB$, where $B$ is a positive Hermitian matrix and $U$ is unitary (or, if $A$ is not square, an isometry). This paper shows that the ability to apply a Hamiltonian $\pmatrix{ 0 & A^\dagger \cr A & 0 \cr} $ translates into the ability to perform the transformations $e^{-iBt}$ and $U$ in a deterministic fashion. We show how to use the quantum polar decomposition algorithm to solve the quantum Procrustes problem, to perform pretty good measurements, to find the positive Hamiltonian closest to any Hamiltonian, and to perform a Hamiltonian version of the quantum singular value transformation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
