A Note on Quantum Gates SWAP and iSWAP in Higher Dimensions

Authors

  • Arash Pourkia College College of Engineering and Technology, American University of the Middle East, Kuwait.

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i3.4824

Keywords:

Qudits, Quantum logic gates, Universal gates, Entangling gates.

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.

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Published

2023-07-30

Issue

Section

Nonlinear Analysis

How to Cite

A Note on Quantum Gates SWAP and iSWAP in Higher Dimensions. (2023). European Journal of Pure and Applied Mathematics, 16(3), 1695-1704. https://doi.org/10.29020/nybg.ejpam.v16i3.4824