发表机构
Simon Fraser University; University of Waterloo（西蒙菲莎大学; 滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了一个五量子比特门作为反例，证明广义半Clifford猜想错误，该门位于Clifford层级第五层但非广义半Clifford，并揭示层级在逆运算下不封闭。
AI 中文摘要
Clifford层级是量子门集合的一个嵌套序列，这些量子门可以在标准量子纠错方案中通过门隐形传态进行容错执行。这些门的重要性促使了对它们结构的众多研究。Zeng-Chen-Chuang在2007年猜想所有层级门都是广义半Clifford的，即对于Clifford门$C_1, C_2$、一个置换门$\Pi$和一个对角门$D$，具有形式$C_1 \Pi D C_2$；Beigi-Shor在2008年证明这对所有第三层级的门成立。我们构造了一个五量子比特门，它位于Clifford层级的第五层，但不是广义半Clifford的。我们不仅简单地展示和验证我们针对广义半Clifford猜想的反例，还展示了如何推导出其形式。我们的反例还证明了Clifford层级在逆运算下不封闭。
英文摘要
The Clifford hierarchy is a nested sequence of sets of quantum gates that can be fault-tolerantly performed using gate teleportation within standard quantum error correction schemes. The importance of these gates has motivated numerous studies of their structure. Zeng-Chen-Chuang conjectured in 2007 that all hierarchy gates are generalised semi-Clifford, i.e. take the form $C_1 ΠD C_2$ for Clifford gates $C_1, C_2$, a permutation gate $Π$, and a diagonal gate $D$; Beigi-Shor proved in 2008 that this holds for all third-level gates. We construct a five-qubit gate that is in the fifth level of the Clifford hierarchy but is not generalised semi-Clifford. Rather than simply present and verify our counterexample to the generalised semi-Clifford conjecture, we show how its form can be deduced. Our counterexample also demonstrates that the Clifford hierarchy is not closed under inverses.
CommentsPreliminary draft. Improved exposition forthcoming
