Fault-tolerant quantum computation for local leakage faults

We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage by using appropriate leakage-reduction units such as quantum teleportation. The leakage noise is described microscopically, by Hamiltonian couplings, and the noise is treated coherently, similar to general non-Markovian noise analyzed in Refs. {Terhal04} and {Aliferis05b}. We describe ways to limit the use of leakage-reduction units while keeping the quantum circuits fault-tolerant and we also discuss how leakage reduction by teleportation is naturally achieved in measurement-based computation.