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A protocol called zero-fidelity was recently proposed as an approximation tothe process fidelity. It can be understood as the zeroth-order processfidelity. It remedies problems of the process fidelity such as complexexperimental settings and long running times. However, like the processfidelity, zero-fidelity is also not robust to state preparation and measurement(SPAM) errors. This limits both protocols' usefulness for real devices. Here,we investigate how SPAM errors affect the zero-fidelity for two operationchannels: one channel containing controlled-NOT gates and the other containingcontrolled-Z gates. Then, we compare these two channels by checking thedifference in the zero-fidelities between them. Finally, to make thezero-fidelity protocol independent of SPAM errors, we combine it with therandomized benchmarking (RB) protocol.

Making the zeroth-order process fidelity independent of state preparation and measurement errors