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M. Ge, K. Xue, Yong-Shi Wu (1994)
YANG-BAXTERIZATION AND ALGEBRAIC STRUCTURES
(1989)
Adv. Ser. Math. Phys
(2003)
Inf. Proc
L. Kauffman, S. Lomonaco (2004)
Braiding operators are universal quantum gatesNew Journal of Physics, 6
N. Jing, M. Ge, Yong-Shi Wu (1991)
A new quantum group associated with a ‘nonstandard’ braid group representationLetters in Mathematical Physics, 21
Michael Freedman (2001)
A Magnetic Model with a Possible Chern-Simons PhaseCommunications in Mathematical Physics, 234
M. Jimbo (1989)
INTRODUCTION TO THE YANG-BAXTER EQUATIONInternational Journal of Modern Physics A, 04
A. Shimony, R. Cohen, M. Horne, J. Stachel (1997)
Potentiality, entanglement and passion-at-a-distance
Yong Zhang, L. Kauffman, M. Ge (2004)
Universal Quantum Gate, Yang-Baxterization and HamiltonianInternational Journal of Quantum Information, 3
S. Hill, W. Wootters (1997)
Entanglement of a Pair of Quantum BitsPhysical Review Letters, 78
L. Faddeev (1982)
INTEGRABLE MODELS IN (1+1)-DIMENSIONAL QUANTUM FIELD THEORY
(2002)
AMS PSAPM/58
M. Freedman, A. Kitaev, Zhenghan Wang (2000)
Simulation of Topological Field Theories¶by Quantum ComputersCommunications in Mathematical Physics, 227
(1967)
Phys. Rev. Lett
M. Nielsen, I. Chuang (1999)
Quantum Computation and Quantum Information
A. U.S (2004)
A New Quantum Group Associated with a ' Nonstandard ' Braid Group Representation
Arxiv: quan-ph/0407224
R. Werner (1989)
Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model.Physical review. A, General physics, 40 8
V. Turaev (1988)
The Yang-Baxter equation and invariants of linksInventiones mathematicae, 92
L. Kauffman (2004)
Teleportation topologyOptics and Spectroscopy, 99
L. Kauffman, S. Lomonaco (2002)
Quantum entanglement and topological entanglementNew Journal of Physics, 4
(1992)
Knot Theory and Its Ramifications
J. Ellis, N. Mavromatos, D. Nanopoulos (2005)
Int. J. Mod. Phys.
(1986)
Commun
(1991)
Proceedings of the NATO Advanced Study Institute and Banff Summer School in Theoretical Physics (Plemum
M. Ge, Yong-Shi Wu, K. Xue (1991)
EXPLICIT TRIGONOMETRIC YANG-BAXTERIZATIONInternational Journal of Modern Physics A, 06
K. Sogo, M. Uchinami, Y. Akutsu, M. Wadati (1982)
Classification of Exactly Solvable Two-Component ModelsProgress of Theoretical Physics, 68
(2001)
Found
M. Ge, K. Xue (1991)
New solutions of Braid group representations associated with Yang–Baxter equationJournal of Mathematical Physics, 32
(1988)
Invent. Math
(2004)
Quantum Information and Computation II Spie Proceedings
R. Brylinski, Goong Chen (2002)
Mathematics of Quantum Computation
(2005)
Opt. Spectrosc
Y. Akutsu, M. Wadati (1987)
Exactly Solvable Models and New Link Polynomials. I. N-State Vertex ModelsJournal of the Physical Society of Japan, 56
L. Kauffman (1991)
Knots And Physics
(1985)
Sov. Math. Dokl
H. Dye (2002)
Unitary Solutions to the Yang–Baxter Equation in Dimension FourQuantum Information Processing, 2
J. Brylinski, R. Brylinski (2001)
Universal quantum gatesarXiv: Quantum Physics
M. Bordewich, M. Freedman, L. Lovász, D. Welsh (2005)
Approximate Counting and Quantum ComputationCombinatorics, Probability and Computing, 14
H. Lee, M. Couture (1988)
A Method to Construct Closed Braids from Links and a New Polynomial for Connected Links
M. Salamon, P. Anderson, A. Cunningham, R. Glosser, John Hoffman, Joseph Izen, Mark Lee, X. Lou, Wolfgang Rindler, Robert Wallace, A. Zakhidov, Y. Gartstein, M. Ishak-Boushaki, Lindsay King, David Lary, A. Malko, Chuanwei Zhang, Jie Zheng, Lunjin Chen, Xingang Chen, Yves Chabal, J. Ferraris, Massimo Fischetti, Tobias Hagge (1929)
PhysicsNature, 123
A. Belavin, V. Drinfel'd (1982)
Solutions of the classical Yang - Baxter equation for simple Lie algebrasFunctional Analysis and Its Applications, 16
M. Ge, L. Gwa, Hong-kang Zhao (1990)
Yang-Baxterization of the eight-vertex model: the braid group approachJournal of Physics A, 23
L. Kauffman, S. Lomonaco (2004)
Quantum knots, 5436
神保 道夫 (1986)
Quantum R matrix for the generalized Toda system
L. Kauffman, S. Lomonaco (2003)
Entanglement criteria: quantum and topological, 5105
P. Aravind (1997)
Borromean Entanglement of the GHZ State
Y. Akutsu, T. Deguchi, M. Wadati (1987)
Exactly Solvable Models and New Link Polynomials. II. Link Polynomials for Closed 3-BraidsJournal of the Physical Society of Japan, 56
(1972)
Annals Phys
C. Schultz (1981)
Solvable q-state models in lattice statistics and quantum field theoryPhysical Review Letters, 46
W. Wootters (1997)
Entanglement of Formation of an Arbitrary State of Two QubitsPhysical Review Letters, 80
V. Drinfeld (1985)
Hopf algebras and the quantum Yang-Baxter equationProceedings of the USSR Academy of Sciences, 32
M. Freedman, M. Larsen, Zhenghan Wang (2000)
A Modular Functor Which is Universal¶for Quantum ComputationCommunications in Mathematical Physics, 227
L.H. Kauffman, S.J. Lomonaco (2003)
Quantum Information and Computation-Spie Proceedings, (21-22 April).
(1998)
Topological Views on Computational Complexity
Hoong-Chien Lee (1990)
Physics, geometry, and topology
Yi Cheng, M. Ge, K. Xue (1991)
Yang-Baxterization of braid group representationsCommunications in Mathematical Physics, 136
L. Kauffman (1999)
Quantum Topology and Quantum Computing
M. Jimbo (1986)
QuantumR matrix for the generalized Toda systemCommunications in Mathematical Physics, 102
R. Baxter (1972)
Partition function of the eight vertex lattice modelAnnals of Physics, 281
M. Couture, Y. Cheng, M. Ge, K. Xue (1991)
NEW SOLUTIONS OF THE YANG-BAXTER EQUATION AND THEIR YANG-BAXTERIZATIONInternational Journal of Modern Physics A, 06
(1990)
A: Math
(1990)
J. Phys. A: Math. Gen
(1987)
J. Phys. Soc. Jap
(1982)
Funcl. Anal. Appl
T. Deguchi, M. Wadati, Y. Akutsu (1990)
Exactly Solvable Models and New Link Polynomials., 11
C. Yang (1967)
Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function InteractionPhysical Review Letters, 19
M. Freedman (2000)
Quantum Computation and the Localization of Modular FunctorsFoundations of Computational Mathematics, 1
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 the unitary solutions of the quantum Yang–Baxter equation via Yang–Baxterization from the solutions of the braid relation. We study Yang–Baxterizations of the non-standard and standard representations of the six-vertex model and the complete solutions of the non-vanishing eight-vertex model. We construct Hamiltonians responsible for the time-evolution of the unitary braiding operators which lead to the Schrödinger equations.
Quantum Information Processing – Springer Journals
Published: Jun 17, 2005
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