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dc.contributor.authorRoberts, Sam
dc.date.accessioned2019-10-04
dc.date.available2019-10-04
dc.date.issued2019-02-28
dc.identifier.urihttp://hdl.handle.net/2123/21192
dc.description.abstractIn recent years, topological phases of matter have presented exciting new avenues to achieve scalable quantum computation. In this thesis, we investigate a class of quantum many-body spin models known as symmetry-protected topological (SPT) phases for use in quantum information processing and storage. We explore the fault-tolerant properties of SPT phases, and how they can be utilized in the design of a quantum computer. Of central importance in this thesis is the concept of quantum error-correction, which in addition to its importance in fault-tolerant quantum computation, is used to characterise the stability of topological phases at finite temperature. We begin with an introduction to quantum computation, quantum error correction, and topological phases of matter. We then focus on the fundamental question of whether symmetry-protected topological phases of matter can exist in thermal equilibrium; we prove that systems protected by global onsite symmetries cannot be ordered at nonzero temperature. Subsequently, we show that certain three-dimensional models with generalised higher-form symmetries can be thermally SPT ordered, and we relate this order to the ability to perform fault-tolerant measurement-based quantum computation. Following this, we assess feasibility of these phases as quantum memories, motivated by the fact that SPT phases in three dimensions can possess protected topological degrees of freedom on their boundary. We find that certain SPT ordered systems can be self-correcting, allowing quantum information to be stored for arbitrarily long times without requiring active error correction. Finally, we develop a framework to construct new schemes of fault-tolerant measurement-based quantum computation. As a notable example, we develop a cluster-state scheme that simulates the braiding and fusion of surface-code defects, offering novel alternative methods to achieve fault-tolerant universal quantum computation.en_AU
dc.publisherUniversity of Sydneyen_AU
dc.publisherScienceen_AU
dc.publisherPhysicsen_AU
dc.rightsThe 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
dc.subjectquantum computationen_AU
dc.subjecttopological ordesen_AU
dc.subjectsymmetryen_AU
dc.subjecterror correctionen_AU
dc.titleSymmetry-Protected Topological Phases for Robust Quantum Computationen_AU
dc.typePhD Doctorateen_AU
dc.type.pubtypeDoctor of Philosophy Ph.D.en_AU


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