  The promise of quantum computing with imperfect qubits relies on the ability
of a quantum computing system to scale cheaply through error correction and
fault-tolerance. While fault-tolerance requires relatively mild assumptions
about the nature of qubit errors, the overhead associated with coherent and
non-Markovian errors can be orders of magnitude larger than the overhead
associated with purely stochastic Markovian errors. One proposal to address
this challenge is to randomize the circuits of interest, shaping the errors to
be stochastic Pauli errors but leaving the aggregate computation unaffected.
The randomization technique can also suppress couplings to slow degrees of
freedom associated with non-Markovian evolution. Here we demonstrate the
implementation of Pauli-frame randomization in a superconducting circuit
system, exploiting a flexible programming and control infrastructure to achieve
this with low effort. We use high-accuracy gate-set tomography to characterize
in detail the properties of the circuit error, with and without the
randomization procedure, which allows us to make rigorous statements about
Markovianity as well as the nature of the observed errors. We demonstrate that
randomization suppresses signatures of non-Markovian evolution to statistically
insignificant levels, from a Markovian model violation ranging from $43\sigma$
to $1987\sigma$, down to violations between $0.3\sigma$ and $2.7\sigma$ under
randomization. Moreover, we demonstrate that, under randomization, the
experimental errors are well described by a Pauli error model, with model
violations that are similarly insignificant (between $0.8\sigma$ and
$2.7\sigma$). Importantly, all these improvements in the model accuracy were
obtained without degradation to fidelity, and with some improvements to error
rates as quantified by the diamond norm.
