One-way quantum computation with four-dimensional photonic qudits

TL;DR

This paper explores the use of four-dimensional photonic qudits, specifically photons as quadbits, for linear optical quantum computation, including state creation and fusion gate mechanisms.

Contribution

It introduces methods for creating hyper-entangled cluster states with quadbits and proposes mechanisms for higher-dimensional fusion gates in linear optical quantum computing.

Findings

Hyper-entangled states can be generated from single photons and Bell pairs.

Non-deterministic methods for state creation are feasible.

Mechanisms for higher-dimensional fusion gates are proposed.

Abstract

We consider the possibility of performing linear optical quantum computation making use of extra photonic degrees of freedom. In particular we focus on the case where we use photons as quadbits. The basic 2-quadbit cluster state is a hyper-entangled state across polarization and two spatial mode degrees of freedom. We examine the non-deterministic methods whereby such states can be created from single photons and/or Bell pairs, and then give some mechanisms for performing higher-dimensional fusion gates.