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arXiv · 2209.15188

Quantum advantage through the magic pentagram problem

Haesol Han·Jeonghyeon Shin·Minjin Choi·Byung Chan Kim·Soojoon Lee
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Abstract

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.

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Haesol Han, Jeonghyeon Shin, Minjin Choi, Byung Chan Kim, Soojoon Lee. 2022-09-30. Quantum advantage through the magic pentagram problem. https://doi.org/10.1007/s11128-022-03684-6

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