Generating Clifford+T circuit ensembles for Solovay-Kitaev and Randomized Compilation (SKaRC)

Error-mitigation techniques such as randomized compiling improve the performance of noisy intermediate-scale quantum (NISQ) devices, but in the future, fully fault-tolerant quantum computing will rely on error-correctable operations drawn from a discrete set of quantum gates. Quantum circuits built using error-correctable operations, such as the popular Clifford+T gate set, may approximate any desired operation to arbitrary precision. However, according to the Solovay-Kitaev theorem, increased approximation precision requires deeper circuits. On the other hand, due to the high error rates associated with their operations, NISQ devices perform best with shallow circuit depths. This may seem to limit the utility of longer, approximate sequences, but in practice, sampling error also contributes to the overall circuit error. As a result, there are achievable circuit depths for NISQ devices that allow us to benefit from Solovay-Kitaev decompositions. We show that by averaging over an ensemble of circuit approximations, error rates improve in both noiseless and noisy simulations. We call this approach SKaRC: Solovay-Kitaev and Randomized Compilation.