  Experiments conducted on open-access cloud-based IBM Quantum devices are
presented for characterizing their fault tolerance using $[4,2,2]$-encoded gate
sequences. Up to 100 logical gates are activated in the IBMQ Bogota and IBMQ
Santiago devices and we found that a $[4,2,2]$ code's logical gate set may be
deemed fault-tolerant for gate sequences larger than 10 gates. However, certain
circuits did not satisfy the fault tolerance criterion. In some cases, the
encoded-gate sequences show a high error rate that is lower bounded at $\approx
0.1$, whereby the error inherent in these circuits cannot be mitigated by
classical post-selection. A comparison of the experimental results to a simple
error model reveals that the dominant gate errors cannot be readily represented
by the popular Pauli error model. Finally, it is most accurate to assess the
fault tolerance criterion when the circuits tested are restricted to those that
give rise to an output state with a low dimension.
