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 d2, 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. 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±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