Topological wormholes

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, $2$D lattice. We show that these defects are capable of encoding logical qubits and can be used to perform all gates in the Clifford group.

arXiv comment5 + 1 pages, 10 figures. Comments welcome

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• Logical blocks for fault-tolerant topological quantum computation
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• Fault-tolerant gates on hypergraph product codes
• Partitioning qubits in hypergraph product codes to implement logical gates
• Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
• Non-Abelian statistics with mixed-boundary punctures on the toric code
• No Strings Attached: Boundaries and Defects in the Cubic Code
• A graph-based formalism for surface codes and twists