Purification of large bicolorable graph states

Abstract

We describe purification protocols for bicolorable graph states. The protocols scale efficiently for large graph states. We introduce a method of analysis that allows us to derive simple recursion relations characterizing their behavior as well as analytical expressions for their thresholds and fixed-point behavior. We introduce two purification protocols with high threshold. They can, for graph degree 4, tolerate 1% (3%) gate error or 20% (30%) local error.