Fault-tolerant computing with biased-noise superconducting qubits: A case study

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.