  Accurate and robust estimation of quantum process properties is crucial for
quantum information processing and quantum many-body physics. Combining
classical shadow tomography and randomized benchmarking, Helsen et al.
introduced a method to estimate the linear properties of quantum processes. In
this work, we focus on the estimation protocols of nonlinear process properties
that are robust to state preparation and measurement errors. We introduce two
protocols, both utilizing random gate sequences but employing different
post-processing methods, which make them suitable for measuring different
nonlinear properties. The first protocol offers a robust and sound method to
estimate the out-of-time-ordered correlation, as demonstrated numerically in an
Ising model. The second protocol estimates unitarity, effectively
characterizing the incoherence of quantum channels. We expect the two protocols
to be useful tools for exploring quantum many-body physics and characterizing
quantum processes.
