论文标题
Qutrit Metapclic大门是Clifford+T的子集
Qutrit metaplectic gates are a subset of Clifford+T
论文作者
论文摘要
Clifford+T是一个流行的通用门集用于量子计算的量子计算，因为这可以在许多容忍耐故障的体系结构上很容易实现。对于Qutrits来说，有一个等效的T门，就像其Qubit类似物一样，使Clifford+T近似通用，可以通过魔术状态注射，并支持魔术状态蒸馏。但是，据称，Qutrit的更好的门可能是Clifford+R，其中R = Diag（1,1，-1）是元容器，因为使用R门比T门更容易地实现了某些协议和门。 In this paper we show that when we have at least two qutrits, the qutrit Clifford+R unitaries form a strict subset of the Clifford+T unitaries, by finding a direct decomposition of $R \otimes \mathbb{I}$ as a Clifford+T circuit and proving that the T gate cannot be exactly synthesized in Clifford+R.这表明实际上，T门与R门的功能至少强大，达到恒定因素。此外，我们还表明，无法找到R Gate的单Qutrit Clifford+T分解，从而使我们的结果紧张。
A popular universal gate set for quantum computing with qubits is Clifford+T, as this can be readily implemented on many fault-tolerant architectures. For qutrits, there is an equivalent T gate, that, like its qubit analogue, makes Clifford+T approximately universal, is injectable by a magic state, and supports magic state distillation. However, it was claimed that a better gate set for qutrits might be Clifford+R, where R=diag(1,1,-1) is the metaplectic gate, as certain protocols and gates could more easily be implemented using the R gate than the T gate. In this paper we show that when we have at least two qutrits, the qutrit Clifford+R unitaries form a strict subset of the Clifford+T unitaries, by finding a direct decomposition of $R \otimes \mathbb{I}$ as a Clifford+T circuit and proving that the T gate cannot be exactly synthesized in Clifford+R. This shows that in fact the T gate is at least as powerful as the R gate, up to a constant factor. Moreover, we additionally show that it is impossible to find a single-qutrit Clifford+T decomposition of the R gate, making our result tight.
