Tyler Ellison (Purdue), "Universal quantum computation with group surface codes"

Abstract: The surface code is one of the leading approaches to building a fault-tolerant quantum computer. A central challenge for the surface code is implementing non-Clifford operations -- unitaries which map Pauli operators to non-Pauli operators. In this talk, I will introduce group surface codes, which are a natural generalization of the usual Z_2 surface code and can be understood as quantum double models of finite groups with specific boundary conditions. I will show that group surface codes, for suitably chosen groups, can be leveraged to perform non-Clifford gates in the Z_2 surface code. Time permitting, I will describe three strategies for completing a universal gate set using group surface codes: through magic state preparation, using transversal non-Clifford gates, and by sliding group surface
codes. These strategies extend recent efforts in performing universal quantum computation in topological orders without the braiding of anyons. Moreover, they show how certain group surface codes allow us to bypass the restrictions set by the Bravyi-König theorem, which limits the computational power of topological Pauli stabilizer models.
This is based on work in progress with Naren Manjunath, Vieri Mattei, and Apoorv Tiwari.