Loss Tolerance with a Concatenated Graph State

A new way of addressing loss errors is introduced which combines ideas from measurement-based quantum computation and concatenated quantum codes, allowing for universal quantum computation. It is shown that for the case where leakage is detected upon measurement, the scheme performs well under 23% loss rate. For loss rates below 10%, this approach performs better than the best scheme known up to date [Phys. Rev.Lett., 97(12):120501]. If lost qubits are tagged prior to measurement, it can tolerate up to 50% loss. The overhead per logical qubit is shown to be significantly lower than other schemes. The obtention of the threshold is entirely analytic.