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11
Teleportation topology
 Optics and Spectroscopy
, 2005
"... The paper discusses teleportation in the context of comparing quantum and topological points of view. 1 ..."
Abstract

Cited by 8 (1 self)
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The paper discusses teleportation in the context of comparing quantum and topological points of view. 1
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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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
and
, 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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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. 0
States, Knots and Networks
, 2004
"... This paper details possible extensions and also limitations of the Aravind Hypothesis for comparing quantum measurement with classical topological measurement. We detail a separate, network model for quantum evolution and measurement, where the background space is replaced by an evolving network. In ..."
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This paper details possible extensions and also limitations of the Aravind Hypothesis for comparing quantum measurement with classical topological measurement. We detail a separate, network model for quantum evolution and measurement, where the background space is replaced by an evolving network. In this model there is an analog of the Aravind Hypothesis that promises to directly illuminate relationships between physics and topology.
and
, 2007
"... 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 ..."
Abstract
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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. 0
and
, 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 ..."
Abstract
 Add to MetaCart
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. 0
and
, 2004
"... This paper is an exploration of the role of unitary braiding operators in quantum computing. We show that a single specific solution R of the YangBaxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non ..."
Abstract
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This paper is an exploration of the role of unitary braiding operators in quantum computing. We show that a single specific solution R of the YangBaxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new nontrivial invariant of braids, knots, and links. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and In this paper, we prove that solutions to the (braiding) YangBaxter equation together with local unitary two dimensional operators form a universal set of quantum gates. In the first version of this result, we generate CNOT using two solutions to the YangBaxter equation. In the second version, we
and
, 2004
"... This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the YangBaxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same ..."
Abstract
 Add to MetaCart
This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the YangBaxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new nontrivial invariant of braids, knots, and links. Other solutions of the YangBaxter Equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantumentanglement and topological entanglement, and the structure of braiding in a topological quantum field theory. 1
and
, 2004
"... This paper is an exploration of the role of unitary braiding operators in quantum computing. We show that a single specific solution R of the YangBaxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non ..."
Abstract
 Add to MetaCart
This paper is an exploration of the role of unitary braiding operators in quantum computing. We show that a single specific solution R of the YangBaxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new nontrivial invariant of braids, knots, and links. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and In this paper, we prove that certain solutions to the YangBaxter equation together with local unitary two dimensional operators form a universal set of quantum gates. In the first version of this result, we generate CNOT using a solution to the algebraic YangBaxter equation. In the second version,
and
, 2004
"... This paper is an exploration of the role of unitary braiding operators in quantum computing. We show that a single specific solution R of the YangBaxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non ..."
Abstract
 Add to MetaCart
This paper is an exploration of the role of unitary braiding operators in quantum computing. We show that a single specific solution R of the YangBaxter Equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new nontrivial invariant of braids, knots, and links. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and In this paper, we prove that certain solutions to the YangBaxter equation together with local unitary two dimensional operators form a universal set of quantum gates. In the first version of this result, we generate CNOT using a solution to the algebraic YangBaxter equation. In the second version,