  In a recent work a quantum error mitigation protocol was applied to the
expectation values obtained from circuits on the IBM Eagle quantum processor
with up $127$ - qubits with up to $60 \; - \; \mbox{CNOT}$ layers. To benchmark
the efficacy of this quantum protocol a physically motivated quantum circuit
family was considered that allowed access to exact solutions in different
regimes. The family interpolated between Clifford circuits and was additionally
evaluated at low depth where exact validation is practical. It was observed
that for highly entangling parameter regimes the circuits are beyond the
validation of matrix product state and isometric tensor network state
approximation methods. Here we compare the experimental results to matrix
product operator simulations of the Heisenberg evolution, find they provide a
closer approximation than these pure-state methods by exploiting the closeness
to Clifford circuits and limited operator growth. Recently other approximation
methods have been used to simulate the full circuit up to its largest extent.
We observe a discrepancy of up to $20\%$ among the different classical
approaches so far, an uncertainty comparable to the bootstrapped error bars of
the experiment. Based on the different approximation schemes we propose
modifications to the original circuit family that challenge the particular
classical methods discussed here.
