QLunch: Ben Brown

Speaker: Ben Brown

Title: Universal quantum computing in two dimensions without getting tied in knots

Abstract: Large-scale quantum computing requires a universal set of fault-tolerant logical operations. Here we show that we can complete a universal set of logic gates with an Abelian topological phase by transforming its ground state onto that of a non-Abelian phase, and subsequently reversing the operation. We show concretely that this process maps the ground-space of an Abelian phase onto a useful magic state. We show how this process can be made fault-tolerant using a just-in-time decoder. In addition, we show how known proposals for non-Clifford operations for two-dimensional codes can be interpreted as a transition between different topological phases, thereby unifying the theory of non-Clifford gates with Abelian codes. Conversely, we argue that this equivalence gives us a path to robustly prepare non-Abelian phases with apparatus that is available with near-term experiments.