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

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This allows construction of a quantum “loop” model with non-abelian braiding, thequantum Potts net.Fendley and Fradkin; Fidkowski, Freedman, Nayak, Walker and Wang; see also Levin and WenThe degrees of freedom are branching nets with only trivalent vertices allowed, e.g.One creates two Fibonacci anyons by cutting one of the strands, i.e. each anyoncorresponds to the end of a strand.40
The new proof of the golden identity using quantum topology exploits the chromaticalgebra plus two special properties valid at special values of Q.1. The Jones-Wenzl projector exists when q is a root of unity. When q = e iπ/5 , i.e.Q = τ + 1, setting it to zero givesτ =+This can be viewed as an identity for chromatic polynomials.41
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 12 and 13: Even more spectacular phenomena tha
Page 14 and 15: We need to understand fusion: what
Page 16 and 17: φ × φ = I + φPrecise meaning in
Page 18 and 19: To make a qubit requires 4 Fibonacc
Page 20 and 21: One can find the braiding and fusin
Page 22 and 23: A simple way of satisfying the cons
Page 24 and 25: These relations can all be treated
Page 26 and 27: The problem: find a quantum Hamilto
Page 28 and 29: The leading candidate wavefunction
Page 30 and 31: A (hopefully not unique) procedure
Page 32 and 33: The excitations with non-abelian br
Page 34 and 35: These nets can be described using t
Page 36 and 37: Such loops satisfy a property under
Page 38 and 39: We find models with deconfined Fibo
Page 42 and 43: 2. Level-rank duality: Here we expl

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

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