Claire Levaillant, USC

Abstract: I will introduce topological quantum computation with quasi-particles called "anyons". This is Microsoft's approach to building a quantum computer and this work was done with Michael Freedman and his lab Station Q.
A result by Renee and Jean-Luc Brylinski states that in order to be able to perform any unitary operation on a quantum computer, a universal set of 1-qubit gates together with only one 2-qubit entangling gate are sufficient.
The operations on a topological quantum computer are realized by interchanging the relative positions of the particles ("braiding them") and measuring their collective topological charge.
For some anyonic systems, operations performed on 1-qubits by braiding only, lead to a finite set of unitary matrices (called "quantum gates"). This is the case with so-called SU(2)_4 anyons. In order to obtain a dense subgroup of SU(2) instead, measurements operations must be added, and must be added smartly so as to collapse quantum information in a unitary way. In case of undesired measurement outcomes, recovery procedures should exist.
In this talk, we will present a scheme using braiding supplemented by measurements of SU(2)_4 anyons providing universality of 1-qubit gates.

The talk will be made accessible to a wide audience. Anyone in the department should feel free to attend.