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 qubit loss 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 \cite{varnava2006loss}. 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.