Randomized benchmarking protocol for dynamic circuits

Dynamic circuit operations (measurements with feedforward) are important components for future quantum computing efforts, but lag behind gates in the availability of characterization methods. Here we introduce a series of dynamic circuit benchmarking routines based on interleaving dynamic circuit operation blocks $\mathcal{F}$ in one-qubit randomized benchmarking sequences of data qubits. $\mathcal{F}$ spans between the set of data qubits and a measurement qubit and may include feedforward operations based on the measurement. We identify six candidate operation blocks, such as preparing the measured qubit in $|0\ensuremath{\rangle}$ and performing a $Z$-Pauli on the data qubit conditioned on a measurement of ``1''. Importantly, these blocks provide a methodology to accumulate readout assignment errors in a long circuit sequence. We also show the importance of dynamical decoupling in reducing $ZZ$ crosstalk and measurement-induced phase errors during dynamic circuit blocks. When measured on an IBM Eagle device with appropriate dynamical decoupling, the results are consistent with measurement assignment error and the decoherence of the data qubit as the leading error sources.