Topological Quantum Computation (Google e-bog)
"Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators. This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter."--Publisher's description.
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Topology and Physics: Proceedings of the Nankai International Conference in ...
Kevin Lin,Zhenghan Wang,Weiping Zhang
Ingen eksempelvisning - 2008
3-manifold 6j symbols abelian algebras algorithm axiom bit string boundary braid group braid group representations called Chern-Simons theory classical colored deﬁned deﬁnition denoted diﬀerent edge eﬀect eﬃciently eigenvalues electron encoded F-matrices Fibonacci Fibonacci theory ﬁnite ﬁrst ﬁxed formal diagram FQH liquids Frobenius-Schur indicators fusion category fusion rule fusion tree basis gate set given graph graphical calculus Hamiltonian hence Hermitian Hilbert space Hom(x,y integer isomorphism Jones algebroids Jones evaluations Jones polynomial Jones representation Kauﬀman bracket label set Lagrangian lattice link diagram mapping class group matrix modular functor morphism non-abelian anyons oriented 3-manifold particles path integral phases of matter physical quantum circuit quantum dimension quantum invariants quantum system qubit Reshetikhin-Turaev root of unity self-dual simple objects subspace tensor categories tensor product Theorem TLJ(A TLn(A topological phases topological quantum computation toric code TQFTs trivial UMTC vector space wave functions