Cluster-state creation in liquid-state NMR

Abstract

The subject of this thesis is devoted to a class of multiparticle entangled states known as the cluster-states. In particular, we focused on a system of four spins and studied the entanglement properties of a four-qubit cluster-state, using a set of entanglement measures for quantifying multipartite entanglement. We then experimentally prepared the linear cluster-state in a liquid NMR sample of crotonic acid, by applying a set of pulses generated by the Gradient Ascent Pulse Engineering (GRAPE) algorithm on a temporally averaged pseudo-pure state of four carbon spins. While our spectral results were consistent with the creation of a linear cluster-state, the reconstruction of the experimental density matrix via a full state tomography of the system revealed additional challenges in the detection of certain desired spin terms. These problems must be overcome before the system could be studied quantitatively.