Randomized Benchmarking of Majorana Based Qubits

We analyze randomized benchmarking (RB) in the context of Majorana zero mode (MZM) based qubits. In particular, we focus on the recently proposed MZM hexon architectures which allow for topologically protected measurement-based braiding gates at the expense of a non-minimal encoding of the qubit. This leads to a departure from standard RB in that the gates depend on non-deterministic measurement outcomes and are prone to non-trivial unitary effects due to the larger encoding. Furthermore, the effect of imperfect measurement bases and the resulting projections must be considered. In this work we adapt the framework of RB to MZM qubits with measurement-based gates and expand upon it by offering a protocol to directly characterize the fidelity of the underlying measurements themselves.