  Non-Markovian noise presents a particularly relevant challenge in
understanding and combating decoherence in quantum computers, yet is
challenging to capture in terms of simple models. Here we show that a simple
phenomenological dynamical model known as the post-Markovian master equation
(PMME) accurately captures and predicts non-Markovian noise in a
superconducting qubit system. The PMME is constructed using experimentally
measured state dynamics of an IBM Quantum Experience cloud-based quantum
processor, and the model thus constructed successfully predicts the
non-Markovian dynamics observed in later experiments. The model also allows the
extraction of information about cross-talk and measures of non-Markovianity. We
demonstrate definitively that the PMME model predicts subsequent dynamics of
the processor better than the standard Markovian master equation.
