Quantum Error Correcting Codes in Eigenstates of Translation-Invariant Spin Chains

Understand

Quantum error correction was invented to allow for fault-tolerant quantum computation.

• Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces.
• More recently, in the context of the AdS/CFT correspondence, it has been argued that eigenstates of CFTs with a holographic dual should also form QECCs.
• These two examples raise the question of how generally eigenstates of many-body models form quantum codes.