How many randomly compiled circuits do we need to see a benefit from RC?

A valid question to ask is, how many randomly compiled circuits do we need to see a benefit from randomized compiling (RC)? We re-analyzed the random circuit sampling data presented on the RC project page to answer this question. For each circuit depth (K) in which we generated random circuits, we computed the convergence of the RC TVD as a function of the number of random compilations. We found that, on average, we only needed ~5 – 10 RC circuits to converge to an optimal result, as opposed to the 20 that were actually used. This is very promising for those that are hoping to utilize RC for improving quantum algorithms, without the added expense of longer runtimes.