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Quantum Field Theories, Topological Materials, and Topological Quantum Computing.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Quantum Field Theories, Topological Materials, and Topological Quantum Computing./
作者:	Ilyas, Muhammad.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	303 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-07, Section: B.
Contained By:	Dissertations Abstracts International83-07B.
標題:	Applied physics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28861527
ISBN:	9798759991779

Quantum Field Theories, Topological Materials, and Topological Quantum Computing.
Ilyas, Muhammad.

Quantum Field Theories, Topological Materials, and Topological Quantum Computing. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 303 p.

Source: Dissertations Abstracts International, Volume: 83-07, Section: B.

Thesis (Ph.D.)--Portland State University, 2021.

This item must not be sold to any third party vendors.

A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with the environment. It is a real challenge to completely isolate a quantum system to make it free of decoherence. This problem can be circumvented by the use of topological quantum phases of matter. These phases have quasiparticles excitations called anyons. The anyons are charge-flux composites and show exotic fractional statistics. When the order of exchange matters, then the anyons are called non-Abelian anyons. Majorana fermions in topological superconductors and quasiparticles in some quantum Hall states are non-Abelian anyons. Such topological phases of matter have a ground state degeneracy. The fusion of two or more non-Abelian anyons can result in a superposition of several anyons. The topological quantum gates are implemented by braiding and fusion of the non-Abelian anyons. The fault-tolerance is achieved through the topological degrees of freedom of anyons. Such degrees of freedom are non-local, hence inaccessible to the local perturbations. In this dissertation, we provide a comprehensive review of the fundamentals of logic design in topological quantum computing. The braid group and knot invariants in the skein theory are discussed. The physical insight behind the braiding is explained by the geometric phases and the gauge transformation. The mathematical models for the fusion and braiding are presented in terms of the category theory and the quantum deformation of the recoupling theory. The topological phases of matter are described by the topology of band structure. The wave function of quasiparticles in the quantum Hall effect and the theory of Majorana fermions in topological superconductors are also discussed. The dynamics of the charge-flux composites and their Hilbert space are expressed through the Chern-Simons theory and the two-dimensional topological quantum field theory. The Ising and Fibonacci anyonic models for binary gates are briefly given. Ternary logic gates are more compact than their binary counterparts and naturally arise in a type of anyonic model called the metaplectic anyons. We reduced the quantum cost of the existing ternary quantum arithmetic gates and proposed that these gates can be implemented with the metaplectic anyons.

ISBN: 9798759991779Subjects--Topical Terms:

3343996
Applied physics.
Subjects--Index Terms:

Metaplectic Anyons

Quantum Field Theories, Topological Materials, and Topological Quantum Computing.
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300 $a 303 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-07, Section: B.
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502 $a Thesis (Ph.D.)--Portland State University, 2021.
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520 $a A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with the environment. It is a real challenge to completely isolate a quantum system to make it free of decoherence. This problem can be circumvented by the use of topological quantum phases of matter. These phases have quasiparticles excitations called anyons. The anyons are charge-flux composites and show exotic fractional statistics. When the order of exchange matters, then the anyons are called non-Abelian anyons. Majorana fermions in topological superconductors and quasiparticles in some quantum Hall states are non-Abelian anyons. Such topological phases of matter have a ground state degeneracy. The fusion of two or more non-Abelian anyons can result in a superposition of several anyons. The topological quantum gates are implemented by braiding and fusion of the non-Abelian anyons. The fault-tolerance is achieved through the topological degrees of freedom of anyons. Such degrees of freedom are non-local, hence inaccessible to the local perturbations. In this dissertation, we provide a comprehensive review of the fundamentals of logic design in topological quantum computing. The braid group and knot invariants in the skein theory are discussed. The physical insight behind the braiding is explained by the geometric phases and the gauge transformation. The mathematical models for the fusion and braiding are presented in terms of the category theory and the quantum deformation of the recoupling theory. The topological phases of matter are described by the topology of band structure. The wave function of quasiparticles in the quantum Hall effect and the theory of Majorana fermions in topological superconductors are also discussed. The dynamics of the charge-flux composites and their Hilbert space are expressed through the Chern-Simons theory and the two-dimensional topological quantum field theory. The Ising and Fibonacci anyonic models for binary gates are briefly given. Ternary logic gates are more compact than their binary counterparts and naturally arise in a type of anyonic model called the metaplectic anyons. We reduced the quantum cost of the existing ternary quantum arithmetic gates and proposed that these gates can be implemented with the metaplectic anyons.
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653 $a Ternary arithmetic circuits
653 $a Ternary logic design
653 $a Topological materials
653 $a Topological quantum computing
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