Quantum advantage through the magic pentagram problem

TL;DR

This paper introduces the magic pentagram problem, demonstrating a quantum advantage where quantum circuits can solve it with certainty, unlike classical circuits, highlighting a separation in computational power.

Contribution

The paper presents the magic pentagram problem as a new example of quantum-classical separation, based on a nonlocal game, extending previous results with different problems.

Findings

Quantum circuits solve the problem with certainty.

Classical circuits cannot solve the problem.

Establishes a new separation between QNC^0 and NC^0.

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.