Colour centres in diamond have, in recent years, been heralded as a promising platform for realising quantum communication and computing. In particular, attention has been given to generating entanglement between colour centres to enable quantum networking and the generation of highly entangled states. Over the last 5 years, particular interest has been given to the group-IV colour centres in diamond for their attractive optical properties, long spin coherence times and access to long lived nuclear memories. These properties put group-IV colour centres forward as an ideal platform to realise quantum communication and computing via the generation of highly entangled photonic states. In particular, multi-dimensional cluster states are a universal class of entangled state which would enable measurement-based quantum computing and robust, error-tolerant quantum communication, and as such are an especially relevant objective.

This thesis focuses on a route to generating multi-dimensional cluster states with group-IV colour centres in diamond, outlining three main results. The first result demonstrates quantum control of the tin-vacancy colour centre in diamond for the first time. This result verifies that the tin vacancy centre is a viable spin qubit, resolving the question of whether the high spin-orbit coupling of tin would prevent its use as a qubit. The second result focuses on the intrinsic nuclear spin of the group-IV colour centres, provided by the group-IV atom which lies at its centre. Spectral signatures of several group-IV isotopes are identified before resonant measurements allow the coupling strengths to be investigated for both the germanium-vacancy, of interest due to its high spin of 9/2, and the tin-vacancy, of interest due to its optically resolvable hyperfine transitions. The final result presents a proposal on the generation of multi-dimensional cluster states using group-IV colour centres in diamond. This proposal focuses on making use of the strongly coupled, intrinsic nuclear register present within group-IV colour centres to facilitate this, whilst maintaining only a single light-matter interface. This work combines coherent control of the electron with coupling to an intrinsic nuclear spin and gives a route to generating highly entangled states from a single group-IV colour centre in diamond.