A generalized quantum SWAP gate

TL;DR

This paper introduces a generalized SWAP gate for higher-dimensional quantum systems, expanding the capabilities of quantum networks beyond qubits by using controlled-NOT gates for prime-dimensional qudits.

Contribution

It constructs a generalized SWAP gate for prime-dimensional qudits solely from controlled-NOT gates, extending quantum computing operations to higher dimensions.

Findings

Successfully constructs a generalized SWAP gate for prime-dimensional qudits.

Demonstrates the use of controlled-NOT gates to cyclically permute states in higher dimensions.

Provides a foundation for higher-dimensional quantum network design.

Abstract

The SWAP gate plays a central role in network designs for qubit quantum computation. However, there is a view to generalize qubit quantum computing to higher dimensional quantum systems. In this paper we construct a generalized SWAP gate using only instances of the generalized controlled-NOT gate to cyclically permute the states of $d$ qudits for $d$ prime.