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dc.contributor.authorWebster, Paul Thomas
dc.date.accessioned2021-05-28T04:12:10Z
dc.date.available2021-05-28T04:12:10Z
dc.date.issued2021en_AU
dc.identifier.urihttps://hdl.handle.net/2123/25112
dc.description.abstractPerforming quantum computing that is robust against noise will require that all operations are fault-tolerant, meaning that they succeed with high probability even if a limited number of errors occur. We address the problem of fault-tolerantly implementing logical operators on quantum error-correcting codes – operators that apply logic gates to information protected by such codes. Specifically, we investigate what classes of logical operators are possible by particular approaches in important types of codes, especially topological stabiliser codes. We also analyse what fundamental limitations constrain the goal of realising fault-tolerant quantum computing by such implementations and how these limitations can be overcome. We begin by presenting necessary background theory on quantum computing, quantum error-correcting codes and fault tolerance. We then specifically consider the approach to fault tolerance of locality-preserving logical operators in topological stabiliser codes. We present a method for determining the set of such operators admitted by a wide range of such codes and apply this method to important examples such as surface codes and colour codes. Next, we consider the alternative approach of implementing logical operators in topological stabiliser codes with defects, especially by the technique of braiding. We show that such approaches are fundamentally limited, but that effective schemes can nonetheless be constructed, both within these limitations and by circumventing them. We then consider fault tolerance in a more general context. We prove a highly general no-go theorem in this context, applicable to a wide range of stabiliser codes. We also show that this proof illuminates how it can be circumvented and provides perspective on a range of fault-tolerant schemes. Finally, we conclude by reviewing how these results collectively address our research questions and suggesting future work.en_AU
dc.subjectquantum computingen_AU
dc.subjecterror correctionen_AU
dc.subjectfault toleranceen_AU
dc.titleFault-Tolerant Logical Operators in Quantum Error-Correcting Codesen_AU
dc.typeThesis
dc.type.thesisDoctor of Philosophyen_AU
dc.rights.otherThe author retains copyright of this thesis. It may only be used for the purposes of research and study. It must not be used for any other purposes and may not be transmitted or shared with others without prior permission.en_AU
usyd.facultySeS faculties schools::Faculty of Science::School of Physicsen_AU
usyd.degreeDoctor of Philosophy Ph.D.en_AU
usyd.awardinginstThe University of Sydneyen_AU
usyd.advisorBARTLETT, STEPHEN


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