Feedback-stabilised quantum states in a mixed-species ion system

Trapped ions are among the leading platforms for realising quantum information processing (QIP). One major challenge in constructing a large-scale QIP device will be to incorporate feedback techniques for performing quantum error correction. This thesis describes the development of a novel classical control system for ion trap quantum computing incorporating powerful real-time processing, and its use in performing a number of experiments involving such processing which form crucial building blocks for stabilizing large-scale ion trap systems. A second major component is the demonstration of multi-qubit quantum control in mixed-species ion chains, which allowed low-crosstalk error-check operations to be performed over tens of cycles in a multi-qubit system for the first time. Combined with feedback this allowed the stabilisation of entanglement over extended sequences of operations. The technical advances in the thesis are a set of control hardware and related firmware and software that is specifically designed to meet the needs of quantum error correction. It enables advanced sequences of measurement, real-time decision making and parameter adjustment needed for scalable experiments, with feedback a core element in its design. Together the feedback-capable system and mixed-species setup were used to test new protocols including a single-qubit adaptive phase estimation scheme relying on rapid real-time classical computation and low-latency parameter updates to optimally extract information, outperforming standard non-adaptive fitting in speed and flexibility. Singleand mixed-species gates between calcium and beryllium and associated experimental techniques were investigated using registers of two and three ions, leading to the first gates between qubits encoded in optical and hyperfine transitions, which reached two-qubit fidelities above 96% and three-qubit fidelities of 93.8(5)%. In preparatory steps for further work, a single-species dissipative protocol was used to prepare an entangled steady-state using a new approach devised in our group, while ion transport and separation experiments with up to four single-species and two mixedspecies ions into wells 800μm apart at excitations below ten quanta was implemented and optimised. The main scientific result of the thesis is the demonstration of the repeated extraction of quantum correlations from a pair of beryllium ions using a calcium ancilla qubit. This type of correlation measurement is critical for performing fault-tolerant algorithms. The measurement was then combined with real-time feedback in order to stabilize beryllium qubits in both subspaces and in entangled states, for sequences including up to fifty rounds of feedback, an order of magnitude more than previous work. Information on the major infidelities in the protocols was extracted from the measurement outcome correlations. This thesis concludes with an outlook for extending the role of both classical and quantum feedback in trapped-ion QIP experiments. This is the second edition of the thesis, released on the 27th of September 2018, incorporating minor corrections. The first edition was released on the 13th of July 2018.