Topological Quantum Computation from non-abelian ... - Paul Fendley

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In 2+1 dimensions, the statistics comes <strong>from</strong> behavior under braiding. Each particletraces out a worldline in time, and these braid around each other.figure <strong>from</strong> Skjeltorp et alBraiding is a purely topological property.11
Page 1 and 2: Topological Quantum Computationfrom
Page 3: Outline:1. What are non-abelian sta
Page 7 and 8: Errors!In a classical computer, jus
Page 9: In three dimensions, the only stati
Page 13 and 14: Braiding particles with non-abelian
Page 15 and 16: The simplest kind of non-abelian st
Page 17 and 18: This fusion algebra allows us to co
Page 19 and 20: This is why non-abelian statistics
Page 21 and 22: We project the world lines of the p
Page 23 and 24: This gives a representation of the
Page 25 and 26: To ensure finite-dimensional repres
Page 27 and 28: One answer:Fig. 1, Pan et al0.5T e~
Page 29 and 30: Another idea:Much effort has been d
Page 31 and 32: To realize this form of braiding, e
Page 33 and 34: To find a quantum loop model which
Page 35 and 36: The generalization of d-isotopy for
Page 37 and 38: The chromatic algebra satisfiesFend
Page 39 and 40: Graphically,= τ 3/2The two types o
Page 41 and 42: The new proof of the golden identit
Page 43: Conclusions• New identities for t

Topological Quantum Computation from non-abelian ... - Paul Fendley

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