Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work [1], Terhal and DiVincenzo have shown that these circuits elude simulation by efficient classical algorithms under plausible complexity-theoretic assumptions. Here we consider possibilistic simulation [2], a particularly weak form of this task where the goal is to output any string appearing with non-zero probability in the output distribution of the circuit. We show that even for single-qubit Clifford-gate-teleportation circuits this simulation problem cannot be solved by constant-depth classical circuits with bounded fan-in gates. Our results are unconditional and are obtained by a reduction to the problem of computing the parity, a well-studied problem in classical circuit complexity.

中文翻译：

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单量子比特门隐形传态提供量子优势


门隐形传态电路可以说是被认为提供了量子计算优势的最基本计算示例之一：在开创性的工作 [1] 中，Terhal 和 DiVincenzo 已经表明，在合理的复杂性理论假设下，这些电路无法通过高效的经典算法进行模拟。在这里，我们考虑可能性模拟 [2]，这是该任务的一种特别弱的形式，其目标是输出在电路的输出分布中以非零概率出现的任何字符串。我们表明，即使对于单量子比特 Clifford 门传送电路，这个仿真问题也无法通过具有有界扇入门的恒定深度经典电路来解决。我们的结果是无条件的，是通过简化计算奇偶校验问题获得的，奇偶校验是经典电路复杂性中一个经过充分研究的问题。