论文标题
通过产品测量来学习量子图状态
Learning quantum graph states with product measurements
论文作者
论文摘要
我们考虑学习$ n $相同的$ n $ n $ qubit量子图状态的问题。这些图形状态具有相应的图形，每个顶点都具有$ d $附近的顶点。在这里，我们详细详细介绍了一种在此类图状态的多个相同副本上使用产品测量值的明确算法来学习它们。当$ n \ gg d $和$ n = o（d \ log（1/ε） + d^2 \ log n），$此算法正确地以概率至少$1-ε$来了解图形状态。从通道编码理论中，我们发现，对于图形状态上的任意关节测量，任何实现此精度的学习算法都需要至少$ω（\ log（1/ε） + d \ log n）$复制时，当$ d = o（\ sqrt n）$。当每个图状态在每个量子位上遇到相同和独立的去极化错误时，我们还提供$ n $的界限。
We consider the problem of learning $N$ identical copies of an unknown $n$-qubit quantum graph state with product measurements. These graph states have corresponding graphs where every vertex has exactly $d$ neighboring vertices. Here, we detail an explicit algorithm that uses product measurements on multiple identical copies of such graph states to learn them. When $n \gg d$ and $N = O(d \log(1/ε) + d^2 \log n ),$ this algorithm correctly learns the graph state with probability at least $1- ε$. From channel coding theory, we find that for arbitrary joint measurements on graph states, any learning algorithm achieving this accuracy requires at least $Ω(\log (1/ε) + d \log n)$ copies when $d=o(\sqrt n)$. We also supply bounds on $N$ when every graph state encounters identical and independent depolarizing errors on each qubit.
