Topological wormholes: Nonlocal defects on the toric code

Abstract

Locality plays a fundamental role in quantum computation but also severely restricts our ability to store and process quantum information. We argue that this restriction may be unwarranted and re-examine quantum error correcting codes. We proceed to introduce new defects on the surface code called wormholes. These novel defects entangle two spatially separated sectors of the lattice. When anyonic excitations enter the mouth of a wormhole, they emerge through the other mouth. Wormholes thus serve to connect two spatially separated sectors of a flat two-dimensional lattice. We show that these defects are capable of encoding logical qubits and can be used to perform all gates in the Clifford group.