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

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To make a qubit requires 4 Fibonacci anyons. There are two different ways of fusingthese four into an overall identity channel – the two states of a qubit!Namely, when the overall channel is I, when the combination of anyons 1 and 2 fuses tostate φ, then anyons 3 and 4 must also be in the state φ. If anyons 1 and 2 fuse to I,then anyons 3 and 4 must also fuse to I.The system can be in any linear combination of these two states. We can change thestate, by braiding particle 2 around particle 3.This entanglement is possible even if none of the particles are near each other!18
This is why non-abelian statistics allow a fault-tolerant quantum computer.The braiding of particle 2 with particle 3 allows us to do quantum computation. The resultof this braiding depends only on the topological properties of the system: these particlescan be very far from each other.No local perturbation will change the results of the braiding.19
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 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 40 and 41: This allows construction of a quant
Page 42 and 43: 2. Level-rank duality: Here we expl

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

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