Bad Qubits — Learn Quantum by Doing

Multiple choice

Approximate quantum error correction (AQEC) relaxes the exact Knill-Laflamme conditions. The canonical motivating example is amplitude damping (energy decay

|1\rangle \to |0\rangle

) with

\gamma = 1 - \exp(-t/T_1)

. To what order in

\gamma

do small four-qubit codes correct a single amplitude-damping event?

To $O(\gamma)$ residual error, i.e. no suppression at all
Only to leading order, leaving an $O(\gamma^2)$ residual (a quadratic suppression of the dominant error)
Exactly, with zero residual error, since amplitude damping is a Pauli channel
Not at all, because amplitude damping is uncorrectable by any quantum code