论文标题
量子极性分解算法
Quantum polar decomposition algorithm
论文作者
论文摘要
矩阵$ a $的极性分解是$ a = ub $，其中$ b $是阳性的Hermitian矩阵，$ u $是统一的（或者，如果$ a $不是正方形，则是等轴测图）。本文表明，应用汉密尔顿$ \ pmatrix {0＆a^\ dagger \ cr a＆0 \ cr} $的能力转化为执行转换$ e^{ - ibt} $和$ u $的能力。我们展示了如何使用量子极性分解算法来解决量子procrustes问题，执行相当不错的测量，以找到最接近任何哈密顿量的阳性汉密尔顿人，并执行哈密顿式版本的量子奇异价值变换。
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.
