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 talk, based on recent work https://arxiv.org/abs/2103.17243, we present a set of efficient algorithms building on the rigorous mathematical theory of Markovian master equations to analyse and evaluate unknown noise processes from a single (or a few) tomographic snapshot(s). In the case of time-independent Markovian (or nearly Markovian) dynamics, our algorithm outputs the best-fit Lindbladian, i.e., the generator of a memoryless quantum channel which best approximates the tomographic data to within the given precision. In the case of non-Markovian dynamics, it 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, together with a range of 1- and 2-qubit numerics of synthesised noisy tomography data, generated using the Cirq platform, showing that we 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.