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Both entanglement and coherence are key resources for all applications of quantum technologies, from the well-known efforts to create a quantum computer, to research into thermodynamic work extraction. Trapped ions are one of the leading platforms for scalable quantum computing, as the site of many of the earliest quantum logic gates, and now boast the current highest-fidelity gates and longest coherence times of their qubits. This thesis presents three strands of work surrounding the creation, manipulation and verification of coherence and entanglement in trapped ions. Coherence is classified into differing ranks, to better represent the structure of multiple-component superpositions. A certifier for these different levels, analogous to an entanglement witness, is derived from a one-dimensional interference pattern in a generalisation of the Ramsey scheme. This metric cannot produce false positives for high-order coherence, even when the coherence basis cannot be measured directly. It requires significantly fewer experimental resources than alternate schemes that have been proposed, and a demonstration in the motional mode of a single trapped ion is presented, verifying that 3-coherence was created. The Mølmer–Sørensen Bell-state-creation gate in trapped ions is then examined, and its principal sources of frequency errors investigated. A multi-tone extension of the gate is presented, which is numerically optimised to make its entanglement generation robust against errors in the qubit and driving frequencies. This analysis produces a gate that is specifically optimised for the estimated error distributions of the target experiment. Finally, the same Mølmer–Sørensen gate is taken outside the weak-coupling approximation in which it has hitherto been confined. A new method of perturbative expansion is introduced and used to calculate functional constraints on the applied driving fields that can be satisfied to cancel unwanted non-linear terms from the dynamics order-by-order. This new strategy removes a previously fundamental limitation on the speed of trapped-ion entangling gates, and severely relaxes the cooling requirements on the motional modes. Open Access |
