A quantum computer is a proposed device which would be capable of initializing, coherently manipulating, and measuring quantum states with sufficient accuracy to carry out new kinds
of computations. In the standard scenario, a quantum computer is built out of quantum bits, or qubits, two-level quantum systems which replace the ordinary classical bits of a classical
computer. Quantum computation is then carried out by applying quantum gates, the quantum equivalent of Boolean logic gates, to these qubits. The most fundamental barrier to building a
quantum computer is the inevitable errors which occur when carrying out quantum gates and the loss of quantum coherence of the qubits due to their coupling to the environment
(decoherence). Remarkably, it has been shown that in a quantum computer such errors and decoherence can be actively fought using what is known as quantum error correction. A closely
related proposal for fighting errors and decoherence in a quantum computer is to build the computer out of so-called topologically ordered states of matter. These are states of matter
which allow for the storage and manipulation of quantum states with a built in protection from error and decoherence. The excitations of these states are non-Abelian anyons, particle-like
excitations which satisfy non-Abelian statistics, meaning that when two excitations are interchanged the result is not the usual +1 and -1 associated with identical Bosons or Fermions, but
rather a unitary operation which acts on a multidimensional Hilbert space. It is therefore possible to envision computing with these anyons by braiding their world-lines in 2+1-dimensional
spacetime. In this Dissertation we present explicit procedures for a scheme which lives at the intersection of these two approaches. In this scheme we envision a functioning
"conventional" quantum computer consisting of an array of qubits and the ability to carry out quantum gates on these qubits. We then give explicit quantum circuits (sequences of quantum
gates) which can be used to create and maintain a topologically ordered state with non-Abelian anyon excitations using the "conventional" qubits of the computer. Our circuits perform
measurements on these qubits which detect "errors" corresponding to deviations from the topologically ordered ground state of interest. We also give circuits which can be used to move
these errors and eventually fuse them with other errors to eliminate them. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2015. / August 31, 2015. / Error Correction, Fibonacci anyon, Levin-Wen model, Non-Abelian, Quantum Computation / Includes bibliographical references. / Nicholas E. Bonesteel, Professor Directing Dissertation; Philip L. Bowers, University Representative; Jorge Piekarewicz, Committee Member; Kun Yang,
Committee Member; Peng Xiong, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_291279 |
| Contributors | Feng, Weibo (authoraut), Bonesteel, N. E. (professor directing dissertation), Bowers, Philip L., 1956- (university representative), Piekarewicz, Jorge, 1956- (committee member), Yang, Kun, 1967- (committee member), Xiong, Peng (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Physics (degree granting department) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource (113 pages), computer, application/pdf |
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