We analyze the use of the Solovay-Kitaev (SK) algorithm to generate an ensemble of one-qubit rotations over which to perform randomized compilation. We perform simulations to compare the trace distance between the quantum state resulting from an ideal one-qubit $R_Z$ rotation and discrete SK decompositions. We find that this simple randomized gate synthesis algorithm can reduce the approximation error of these rotations in the absence of gate errors in simulation by at least a factor of 2 compared to a naive gate synthesis algorithm. We test the technique under the effects of a simple coherent noise model and find that it can mitigate coherent noise. We also run our algorithm on Sandia National Laboratories' QSCOUT trapped-ion device and find that randomization is able to help in the presence of realistic noise sources.

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• Quantum benchmarking
• Quantum circuits
• Quantum error correction
• Quantum gates