Q Seminar: Lucy Zhang (Perimeter Institute), 'Fibre bundle framework for quantum fault tolerance'

Event Date: 

Friday, May 3, 2013 -
2:30pm to 4:00pm

Event Location: 

  • 2250 Elings Hall

Event Price: 

Free

Event Contact: 

Sean Fraer
Email: seanfr@microsoft.com
Phone: 805-893-8818
Website: Click to Visit

Abstract:

We introduce a differential geometric framework for describing families of quantum error-correcting codes and for understanding quantum fault tolerance. This work unifies the notion of topological fault tolerance with fault tolerance in other kinds of quantum error-correcting codes. In particular, we use fibre bundles with a natural projectively flat connection to study the transformation of codewords under unitary fault-tolerant evolutions. We show that the fault-tolerant logical operations are given by the monodromy group for the bundles with projectively flat connection, which is always discrete. As a concrete realization of the general framework, we construct the bundles explicitly for two examples of fault-tolerant families of operations, the string operators in the toric code and the qudit transversal gates.