  The presence of noise is currently one of the main obstacles to achieving
large-scale quantum computation. Strategies to characterise and understand
noise processes in quantum hardware are a critical part of mitigating it,
especially as the overhead of full error correction and fault-tolerance is
beyond the reach of current hardware. Non-Markovian effects are a particularly
unfavorable type of noise, being both harder to analyse using standard
techniques and more difficult to control using error correction. In this work
we develop a set of efficient algorithms, based on the rigorous mathematical
theory of Markovian master equations, to analyse and evaluate unknown noise
processes.
  In the case of time-independent Markovian (or nearly Markovian) dynamics, our
algorithm outputs the best-fit Lindbladian, i.e. the Lindblad master equation
which best approximates the tomographic data to within the given precision. In
the case of non-Markovian dynamics, our algorithm returns a quantitative and
operationally meaningful measure of non-Markovianity in terms of isotropic
noise addition.
  We provide a Python implementation of all our algorithms, and benchmark these
on a range of 1- and 2-qubit examples of synthesised noisy tomography data,
generated using the Cirq platform. The numerical results show that our
algorithms succeed both in extracting a full description of the best-fit
Lindbladian to the measured dynamics, and in computing accurate measures of
non-Markovianity that match analytical calculations.
