Sequence randomization for single qubit gate synthesis

For fault-tolerant quantum computation, it is necessary to synthesize single qubit rotation gates into an error corrected gate set, usually sequences of Clifford+T gates. Some gate synthesis algorithms such as gridsynth proposed by Ross and Selinger have freedom in the exact decomposition used within the user-desired precision ε. This freedom allows for randomized compilation to improve the accuracy of these algorithms by averaging execution over multiple similar gate sequences. We simulate this simple randomization procedure under a coherent noise model and find it can decrease both approximation error and coherent error across a wide range of desired precisions. Additional intra-sequence randomization can improve accuracy further. We show that executing the algorithm on a near-term trapped ion device using two different physical mechanisms for our single qubit gates results in moderate improvements, though device noise remains a limitation on accuracy in near-term reproductions of fault-tolerant routines.