We present a universal scheme of pulsed operations suitable for theIBM oscillator-stabilized flux qubit comprising the controlled-σz(cphase) gate,single-qubit preparations and measurements. Based on numerical simulations,we argue that the error rates for these operations can be as low as about 0.5%and that noise is highly biased, with phase errors being stronger than all othertypes of errors by a factor of nearly 103. In contrast, the design of a controlled-σx(cnot) gate for this system with an error rate of less than about 1.2% seemsextremely challenging. We propose a special encoding that exploits the noise biasallowing us to implement alogicalcnotgate where phase errors and all othertypes of errors have nearly balanced rates of about 0.4%. Our results illustratehow the design of an encoding scheme can be adjusted and optimized accordingto the available physical operations and the particular noise characteristics ofexperimental devices.@en

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. [1] and [2]. We describe ways to limit the use of leakage-reduction units while keeping the quantum circuits faulttolerant and we also discuss how leakage reduction by teleportation is naturally achieved in measurement-based computation.@en