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

More documents

Recommendations

Info

φ × φ = I + φPrecise meaning in field theory: The operator product expansion of two φ fields containsboth the identity field I and the field φ itself .Precise meaning in conformal field theory: the “fusion coefficients” for the primary fields Iand φ are N I φφ = N φ φφ = 1.Precise meaning for this talk: There are two possible quantum states for two Fibonaccianyons. One has trivial statistics, the other has the braiding properties of a singleFibonacci anyon.16
This fusion algebra allows us to count the number of quantum states for 2Nquasiparticles:1 : I1 : φ2 : φ × φ = I + φ3 : φ × φ × φ = I + φ + φ5 : φ × φ × φ × φ = φ + 2(I + φ)8 : φ × φ × φ × φ × φ = 3I + 5φThe number of states for n particles is the nth Fibonacci number.17
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 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

Create successful ePaper yourself

Delete template?

Save as template?