Topological Quantum Computing

Michael Freedman

2012 AAAS Annual Meeting (16-20 February 2012)

Title: "What topology can contribute to the construction of a quantum computer"

Abstract:  Topology by definition is the discrete residue of geometry. If you like it "error corrects" geometric input and returns a topological type, e.g., input a surface and output its "genus". The TKNN invariant of the integer quantum Hall effect is the first Chern class of a bundle over a momentum torus. The discreteness of this Chern class  is so precise that it can be used to define the Ohm. Topological protection looks very close to realization in the form of 1 and 2 dimensional systems of Majorana fermiions. I will discuss what would be required to build a quantum computer based on this physics.