On Binomial Summations and a Generalised Quantum SWAP Gate

TL;DR

This paper introduces a new quantum gate construction that generalizes the SWAP gate to higher dimensions using only CNOT gates, improving on previous methods in regularity and design.

Contribution

A novel, regular quantum gate construction for higher-dimensional systems that extends the qubit SWAP gate using only CNOT gates, surpassing previous WilNOT gate designs.

Findings

Provides a generalized quantum SWAP gate for higher dimensions.

Constructed entirely from CNOT gates, ensuring simplicity and compatibility.

Improves regularity and structure over existing WilNOT gate methods.

Abstract

We give a quantum gate construction - composed entirely from incidents of the CNOT gate - that generalises the qubit SWAP gate to higher dimensions. This new construction is more regular than and is an improvement on the WilNOT quantum gate construction.