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

We present a universal scheme of pulsed operations suitable for the IBM oscillator-stabilized flux qubit comprising the controlled-sigma(z) (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 other types of errors by a factor of nearly 10(3). In contrast, the design of a controlled sigma(x) (CNOT) gate for this system with an error rate of less than about 1.2% seems extremely challenging. We propose a special encoding that exploits the noise bias allowing us to implement a logical CNOT gate where phase errors and all other types of errors have nearly balanced rates of about 0.4%. Our results illustrate how the design of an encoding scheme can be adjusted and optimized according to the available physical operations and the particular noise characteristics of experimental devices.