**One-way quantum computation in 4-d photonic states** - Jaewoo Joo

We consider the possibility of performing linear optical quantum computation making use of extra photonic degrees of freedom. In particular we focus in the case where we use photons as quartit. The basic building block is a 2-quartit cluster state which is called 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.