Experimental Demonstration of a Cheap and Accurate Phase Estimation.

We demonstrate an experimental implementation of robust phase estimation (RPE) to learn the phase of a single-qubit rotation on a trapped Yb^{+} ion qubit. We show this phase can be estimated with an uncertainty below 4×10^{-4}  rad using as few as 176 total experimental samples, and our estimates exhibit Heisenberg scaling. Unlike standard phase estimation protocols, RPE neither assumes perfect state preparation and measurement, nor requires access to ancillae. We crossvalidate the results of RPE with the more resource-intensive protocol of gate set tomography.