A SWAP gate for qudits

TL;DR

This paper introduces a generalized SWAP gate for qudits of any dimension, extending the qubit SWAP gate with symmetry and simplicity, using only three controlled qudit gates and standard quantum operations.

Contribution

It presents a novel, dimension-independent SWAP gate for qudits that relies on minimal controlled gates and standard quantum transformations.

Findings

The gate is valid for arbitrary-dimensional quantum systems.

It maintains key properties like symmetry and simplicity.

Constructed using Quantum Fourier Transform and d-dimensional CZ gate.

Abstract

We present a quantum SWAP gate valid for quantum systems of an arbitrary dimension. The gate generalizes the CNOT implementation of the SWAP gate for qubits and keeps its most important properties, like symmetry and simplicity. We only use three copies of the same controlled qudit gate. This gate can be built with two standard higher-dimensional operations, the Quantum Fourier Transform and the d-dimensional version of the CZ gate.