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Nonabelian anyons and topological quantum computation
 Reviews of Modern Physics
"... Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are partic ..."
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Cited by 56 (0 self)
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Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles,
qdeformed spin networks, knot polynomials and anyonic topological . . .
, 2006
"... We review the qdeformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. Our methods are rooted in the bracket state sum model for the Jones polynomial. We give our results ..."
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Cited by 22 (9 self)
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We review the qdeformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. Our methods are rooted in the bracket state sum model for the Jones polynomial. We give our results for a large class of representations based on values for the bracket polynomial that are roots of unity. We make a separate and selfcontained study of the quantum universal Fibonacci model in this framework. We apply our results to give quantum algorithms for the computation of the colored Jones polynomials for knots and links, and the WittenReshetikhinTuraev invariant of three manifolds.
A SelfLinking Invariant of Virtual Knots
, 2004
"... In this paper we introduce a new invariant of virtual knots and links that is nontrivial for many virtuals, but is trivial on classical knots and links. The invariant will initially be expressed in terms of a relative of the bracket polynomial [4], and then extracted from this polynomial in terms o ..."
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Cited by 18 (12 self)
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In this paper we introduce a new invariant of virtual knots and links that is nontrivial for many virtuals, but is trivial on classical knots and links. The invariant will initially be expressed in terms of a relative of the bracket polynomial [4], and then extracted from this polynomial in terms of its exponents, particularly for the case of knots. The analog
Universal Quantum Gate, Yang– Baxterization and Hamiltonian
 Int. J. Quant. Inform
, 2005
"... It is fundamental to view unitary braiding operators describing topological entanglements as universal quantum gates for quantum computation. This paper derives a unitary solution of the quantum Yang–Baxter equation via Yang–Baxterization and constructs the Hamiltonian responsible for the timeevolu ..."
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Cited by 11 (7 self)
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It is fundamental to view unitary braiding operators describing topological entanglements as universal quantum gates for quantum computation. This paper derives a unitary solution of the quantum Yang–Baxter equation via Yang–Baxterization and constructs the Hamiltonian responsible for the timeevolution of the unitary braiding operator. Keywords: topological entanglement, quantum entanglement, Yang–Baxterization 1.
Teleportation topology
 Optics and Spectroscopy
, 2005
"... The paper discusses teleportation in the context of comparing quantum and topological points of view. 1 ..."
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Cited by 10 (1 self)
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The paper discusses teleportation in the context of comparing quantum and topological points of view. 1
Braid Group and Temperley–Lieb Algebra, and Quantum . . .
, 2008
"... In this paper, we explore algebraic structures and low dimensional topology underlying quantum information and computation. We revisit quantum teleportation from the perspective of the braid group, the symmetric group and the virtual braid group, and propose the braid teleportation, the teleportatio ..."
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Cited by 8 (3 self)
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In this paper, we explore algebraic structures and low dimensional topology underlying quantum information and computation. We revisit quantum teleportation from the perspective of the braid group, the symmetric group and the virtual braid group, and propose the braid teleportation, the teleportation swapping and the virtual braid teleportation, respectively. Besides, we present a physical interpretation for the braid teleportation and explain it as a sort of crossed measurement. On the other hand, we propose the extended Temperley–Lieb diagrammatical approach to various topics including quantum teleportation, entanglement swapping, universal quantum computation, quantum information flow, and etc. The extended Temperley–Lieb diagrammatical rules are devised to present a diagrammatical representation for the extended Temperley–Lieb category which is the collection of all the Temperley–Lieb algebras with local unitary transformations. In this approach, various descriptions of quantum teleportation are unified in a diagrammatical sense, universal quantum computation is performed with the help of topologicallike features, and quantum information flow is
NonAbelian Anyons and Topological Quantum Computation
, 2007
"... Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles know ..."
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Cited by 8 (1 self)
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Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which
YangBaxterizations, universal quantum gates and Hamiltonians
 Quantum Inf. Process
"... The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinski’s theorem, the unitary solutions of the quantum Yang–Baxter equation can be also related to universal quantum gates. This paper derives ..."
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Cited by 7 (5 self)
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The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinski’s theorem, the unitary solutions of the quantum Yang–Baxter equation can be also related to universal quantum gates. This paper derives unitary solutions of the quantum Yang–Baxter equation via Yang–Baxterization from the solutions of the braid relation. We study Yang–Baxterizations of the nonstandard and standard representations of the sixvertex model and the complete solutions of the nonvanishing eightvertex model. We construct Hamiltonians responsible for the timeevolution of the unitary braiding operators which lead to the Schrödinger equations.
Permutation and Its Partial Transpose
, 2006
"... Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang–Baxter equation, and the isotropic state with an adjustable parameter is found to form a braid representation. The set of permutation’s partial ..."
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Cited by 4 (2 self)
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Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang–Baxter equation, and the isotropic state with an adjustable parameter is found to form a braid representation. The set of permutation’s partial transposes is an algebra called the “PPT ” algebra which guides the construction of multipartite symmetric states. The virtual knot theory having permutation as a virtual crossing provides a topological language describing quantum computation having permutation as a swap gate. In this paper, permutation’s partial transpose is identified with an idempotent of the Temperley–Lieb algebra. The algebra generated by permutation and its partial transpose is found to be the Brauer algebra. The linear combinations of identity, permutation and its partial transpose can form various projectors describing tangles; braid representations; virtual braid representations underlying common solutions of the braid relation and Yang–Baxter equations; and virtual Temperley–Lieb algebra which is articulated from the graphical viewpoint. They lead to our drawing a picture called the “ABPK” diagram describing knot theory in terms of its corresponding algebra, braid group and polynomial invariant. The paper also identifies nontrivial unitary braid representations with universal quantum gates, and derives a Hamiltonian to determine the evolution of a universal quantum gate, and further computes the Markov trace in terms of a universal quantum gate for a link invariant to detect linking numbers.