论文标题
通过魔术五角星问题的量子优势
Quantum advantage through the magic pentagram problem
论文作者
论文摘要
通过两个特定的问题，即2D隐藏的线性函数问题和1D魔法正方形问题，Bravyi等人。最近表明，存在$ \ Mathbf {qnc^0} $和$ \ Mathbf {nc^0} $之间的分离，其中$ \ Mathbf {qnc^0} $和$ \ \ m athbf {nc^0} $是polynomial-size size and Commant-deppth量子的类别，并与commant-deptal量子coundial cirdials cirdical cirdiTs courdials cirdials coundial cirdials coundial cirdial cirdical cirdiTs cy g g。在本文中，我们提出了同一属性的另一个问题，即基于Magic Pentagram游戏的Magic Pentagram问题，这是一个非本地游戏。换句话说，我们表明可以通过$ \ mathbf {qnc^0} $电路来确定问题，但不能通过任何$ \ mathbf {nc^0} $电路来解决问题。
Through the two specific problems, the 2D hidden linear function problem and the 1D magic square problem, Bravyi et al. have recently shown that there exists a separation between $\mathbf{QNC^0}$ and $\mathbf{NC^0}$, where $\mathbf{QNC^0}$ and $\mathbf{NC^0}$ are the classes of polynomial-size and constant-depth quantum and classical circuits with bounded fan-in gates, respectively. In this paper, we present another problem with the same property, the magic pentagram problem based on the magic pentagram game, which is a nonlocal game. In other words, we show that the problem can be solved with certainty by a $\mathbf{QNC^0}$ circuit but not by any $\mathbf{NC^0}$ circuits.
