Quantum theory seminar: Apoorv Tiwari, University of Southern Denmark

Universal quantum computation with group surface codes

In this talk, I will introduce group surface codes, a natural generalization of the Z2 surface code that can be understood as Kitaev quantum double models of finite groups with suitable boundary conditions. Logical gate protocols in this framework decompose into a finite set of elementary operations which involve merging, splitting, preparing and reading out group surface codes. In the language of TQFT, these correspond to elementary spacetime blocks in 2+1-dimensional topological gauge theories. I will present a systematic construction of these TQFT building blocks and analyze the fault tolerance of the associated elementary operations. In this framework a group can be constructively designed to implement a target non-Clifford gate on qubits encoded in the Z2 surface code, yielding new routes toward universal quantum computation without anyon braiding and providing a concrete mechanism for bypassing the Bravyi–König theorem which limits the computational power of topological Pauli stabilizer models.