  We demonstrate that there exists a universal, near-optimal recovery map---the
transpose channel---for approximate quantum error-correcting codes, where
optimality is defined using the worst-case fidelity. Using the transpose
channel, we provide an alternative interpretation of the standard quantum error
correction (QEC) conditions, and generalize them to a set of conditions for
approximate QEC (AQEC) codes. This forms the basis of a simple algorithm for
finding AQEC codes. Our analytical approach is a departure from earlier work
relying on exhaustive numerical search for the optimal recovery map, with
optimality defined based on entanglement fidelity. For the practically useful
case of codes encoding a single qubit of information, our algorithm is
particularly easy to implement.
