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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.
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.
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
Topological Quantum Information Theory
"... This paper is an introduction to relationships between quantum topology and quantum computing. In this paper we discuss unitary solutions to the YangBaxter equation that are universal quantum gates, quantum entanglement and topological entanglement, and we give an exposition of knottheoretic recou ..."
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Cited by 1 (1 self)
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This paper is an introduction to relationships between quantum topology and quantum computing. In this paper we discuss unitary solutions to the YangBaxter equation that are universal quantum gates, quantum entanglement and topological entanglement, and we give an exposition of knottheoretic recoupling theory, its relationship with 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
Quantum YangBaxter equation and constant Rmatrix over Grassmann algebra
, 2005
"... Abstract: Constant solutions to YangBaxter equation are investigated over Grassmann algebra for the case of 6vertex Rmatrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, whe ..."
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Abstract: Constant solutions to YangBaxter equation are investigated over Grassmann algebra for the case of 6vertex Rmatrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when Rmatrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6vertex solutions. The solutions leading to regular Rmatrices which appear in weak Hopf algebras are considered.
gates for quantum computation with
, 2006
"... a universal set of topologically protected ..."
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