Error tolerance and tradeoffs in loss- and failure-tolerant quantum computing schemes

Qubit loss and gate failure are significant problems for the development of scalable quantum computing. Recently various schemes have been proposed for tolerating qubit loss and gate failure. These include schemes based on cluster and parity states. We show that by designing such schemes specifically to tolerate these error types we cause an exponential blow-out in depolarizing noise. We discuss several examples and propose techniques for minimizing this problem. In general this introduces a tradeoff with other undesirable effects. In some cases this is physical resource requirements, while in others it is noise rates.