Computational power of symmetry-protected topological phases (D. Stephen)

Date: Apr 11, 2017
Time: 02:00 PM - 03:00 PM (Local Time Germany)
Speaker: Daivd Stephen
University of British Columbia, Vancouver BC, Canada
Room: Herbert Walther Lecture Hall
Host: MPQ, Theory Division

In many-body physics, many essential properties of a quantum state are determined by the phase of matter in which it resides. Recent years have witnessed tremendous progress in the discovery and classification of quantum phases, and it is thus pertinent to ask: what can a phase of matter be used for?

A standout example in quantum information processing is the use of topological phases for error-resilient quantum computation. The exchange statistics of anyonic excitations present in these phases determine the possible logical gates and also label the topological phase itself.

In this talk, I will make a similar connection for the symmetry-protected topological (SPT) phases in one dimension. I will show that the computational power of quantum states, defined via their use as resources for measurement-based quantum computation (MBQC), is uniform within certain SPT phases. This uniform computational power is determined using the same algebraic structure that classifies the SPT phases, namely group cohomology. These results give insight into the structure of MBQC resource states, and highlight how the classification of quantum phases can contribute to our understanding of the power of quantum computation.