  We extensively test a recent protocol to demonstrate quantum fault tolerance
on three systems: (1) a real-time simulation of five spin qubits coupled to an
environment with two-level defects, (2) a real-time simulation of transmon
quantum computers, and (3) the 16-qubit processor of the IBM Q Experience. In
the simulations, the dynamics of the full system is obtained by numerically
solving the time-dependent Schr\"odinger equation. We find that the
fault-tolerant scheme provides a systematic way to improve the results when the
errors are dominated by the inherent control and measurement errors present in
transmon systems. However, the scheme fails to satisfy the criterion for fault
tolerance when decoherence effects are dominant.
