A theory of single-shot error correction for adversarial noise

Understand

Single-shot error correction is a technique for correcting physical errors using only a single round of noisy check measurements, such that any residual noise affects a small number of qubits.

• We propose a general theory of single-shot error correction and establish a sufficient condition called good soundness of the code's measurement checks.
• Good code soundness in topological (or LDPC) codes is shown to entail a macroscopic energy barrier for the associated Hamiltonian.
• Consequently, 2D topological codes with local checks can not have good soundness.