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

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The idea behind a topological quantum computer to exploit systems with quantumredundancy.In particular, in 2+1 dimensions, identical particles can have some very strikingproperties.8
In three dimensions, the only statistics for identical particles are bosonic and fermionic:ψ(x 1 , x 2 , . . . ) = ±ψ(x 2 , x 1 , . . . )Exchanging twice is a closed loop in configuration space.01010101x 1x 2In three dimensions, this can be adiabatically deformed to the identity.9
Page 1 and 2: Topological Quantum Computationfrom
Page 3: Outline:1. What are non-abelian sta
Page 7: Errors!In a classical computer, jus
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 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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