Ground Subspaces of Topological Phases of Matter as Error Correcting Codes

Understand

Topological quantum computing is believed to be inherently fault-tolerant.

• One mathematical justification would be to prove that ground subspaces or ground state manifolds of topological phases of matter behave as error correction codes with macroscopic distance.
• While this is widely assumed and used as a definition of topological phases of matter in the physics literature, besides the doubled abelian anyon models in Kitaev's seminal paper, no non-abelian models are proven to be so mathematically until recently.
• Cui et al extended the theorem from doubled abelian anyon models to all Kitaev models based on any finite group.