Subspace leakage randomized benchmarking with trapped ions

We present and demonstrate a new method for randomized benchmarking two-qubit gates. In some experiments, this enables simplifications over similar techniques. The core idea is to generate a two-design on d = 2 subspace, naturally spanned by the Mølmer-Sørensen interaction, rather than the entire d = 3 symmetric subspace. This lets us generate the necessary Clifford group elements by combining a small set of gate primitives. With phase control of the gate fields, which is straightforward with microwave gates, we do not need single qubit rotations to generate the necessary the gate set. While we average over a smaller subspace than other methods, directly measuring the population increase of each of the three 'incorrect' computational basis states at the end of the circuit, rather than the decrease of the one 'correct' state, allows us to back out similar information—while enjoying the simplified gate set. Measuring this also tells us the relative contributions of subspace preserving and subspace non-preserving errors to the error budget, which provides useful information about the underlying noise mechanisms.