A Note on Quantum Gates SWAP and iSWAP in Higher Dimensions

IF 1 Q1 MATHEMATICS
Arash Pourkia
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引用次数: 0

Abstract

We present explicit descriptions for the swap gate and the iswap gate in any arbitrary dimension $d \geq 2$, in terms of permutation matrices. Moreover, we unify these gates by introducing a more general gate xSWAP which includes SWAP and iSWAP for $x=1$ and $x=i$ (i.e. $\sqrt{-1}$), respectively. The higher dimensional xSWAP e.g., the swap and iswap gates for $d > 2$ serve as quantum logic gates that operate on two $d$-level qudits. For $d=2$, it is well known that iSWAP unlike SWAP is universal for quantum computing. We will prove this fact for xSWAP in any dimension $d$, when $x \neq \pm 1$. Our explicit representation of xSWAP by a permutation matrix facilitates the proof, greatly.
关于高维量子门SWAP和iSWAP的一点注记
我们用置换矩阵的形式给出了任意维$d\geq2$中交换门和iswap门的显式描述。此外,我们通过引入一个更通用的门xSWAP来统一这些门,该门包括SWAP和iSWAP,分别用于$x=1$和$x=i$(即$\sqrt{-1}$)。更高维的xSWAP,例如$d>2$的交换和iswap门,用作在两个$d$级量子位上操作的量子逻辑门。对于$d=2$,众所周知,与SWAP不同的iSWAP在量子计算中是通用的。当$x\neq\pm1$时,我们将在任何维度$d$中证明xSWAP的这一事实。我们用置换矩阵显式表示xSWAP,极大地简化了证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
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