Thesis (M.S.)--Rochester Institute of Technology, 1993. / Typescript. Includes bibliographical references.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 62-63). Also available via the Internet.

Trapped atomic ions are one of the most promising systems for building a quantum computer -- all of the fundamental operations needed to build a quantum computer have been demonstrated in such systems. The challenge now is to understand and reduce the operation errors to below the 'fault-tolerant threshold' (the level below which quantum error correction works), and to scale up the current few-qubit experiments to many qubits. This thesis describes experimental work concentrated primarily on the first of these challenges. We demonstrate high-fidelity single-qubit and two-qubit (entangling) gates with errors at or below the fault-tolerant threshold. We also implement an entangling gate between two different species of ions, a tool which may be useful for certain scalable architectures. We study the speed/fidelity trade-off for a two-qubit phase gate implemented in ⁴³Ca^+ hyperfine trapped-ion qubits. We develop an error model which describes the fundamental and technical imperfections / limitations that contribute to the measured gate error. We characterize and minimise various error sources contributing to the measured fidelity, allowing us to account for errors due to the single-qubit operations and state readout (each at the 0.1% level), and to identify the leading sources of error in the two-qubit entangling operation. We achieve gate fidelities ranging between 97.1(2)% (for a gate time t_g = 3.8 μs) and 99.9(1)% (for t_g = 100 μs), representing respectively the fastest and lowest-error two-qubit gates reported between trapped-ion qubits by nearly an order of magnitude in each case. We also characterise single-qubit gates with average errors below 10^-4 per operation, over an order of magnitude better than previously achieved with laser-driven operations. Additionally, we present work on a mixed-species entangling gate. We entangle of a single ⁴⁰Ca^+ ion and a single ⁴³Ca^+ ion with a fidelity of 99.8(5)%, and perform full tomography of the resulting entangled state. We describe how this mixed-species gate mechanism could be used to entangle ⁴³Ca^+ and ⁸⁸Sr^+, a promising combination of ions for future experiments.

Thesis (Nucl. E.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographies and index. / by Claudio Daniel Antonini. / Nucl.E.

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<p> In this thesis we develop a mathematical framework to express and reason about properties of fault-tolerant computing systems. The main idea behind this mathematical framework is to use axiomatic theories to specify systems. The standard logical operators allow us to describe the basic behavior of the system, while we use deontic predicates on actions to express prescriptions about the system's behavior. Deontic logics have proved to be useful for reasoning about legal and moral systems, where the situation is more or less similar to fault-tolerance: there exists a set of rules that states what the normal behaviours or scenarios are. Violations arise when these rules are not followed and, as a consequence, some actions must be performed to return to a normal or desirable state. We develop our own deontic logic, keeping in mind that we want to use it for specifying fault-tolerant systems. We investigate the properties of this logic, commenting on those that are relevant to the use of the logic in practice. We provide two different deductive systems; one of them is a standard (Hilbert style) deductive system, while the other one is a tableaux system, which can be applied automatically to prove properties of specifications.</p> <p> In any specification language, it is important to have at hand mechanisms which enable designers to modularize the system description; we investigate how to apply these mechanisms to the logics proposed in this thesis, and, in particular, we focus on how the modularization of specifications affects the local prescriptions of a module (or component). We study the problems that arise from the interaction between components. We show that, in some cases, we can guarantee that the locality of violations in a particular component is preserved. Some examples are provided throughout this thesis to illustrate how the ideas described below can be applied in practice. </p> / Thesis / Doctor of Philosophy (PhD)

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