Non-Markovian Quantum Process Tomography

Quantum devices are rapidly advancing, but headway magnifies the impact of correlated — or non-Markovian — noise. To this effect, progress in characterisation must keep up with intricate quantum behaviour. Conventional tools typically assume a weak or memoryless system-environment interaction, models which break down under a temporally correlated process. A missing piece in the zoo of characterisation procedures is tomography which can completely describe non-Markovian dynamics. Here, we formally introduce a generalisation of quantum process tomography, called process tensor tomography. We manage a practical approach with accurate post-processing algorithms for maximum-likelihood estimation, and make the procedure efficient for low-memory processes, experimentally validated on IBM Quantum devices. Surprisingly, we find deep structures in the noisy dynamics such as higher order temporal quantum correlations, including entanglement in time. We show this characterisation technique leads to superior control by effective accounting of the non-Markovian environment. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation, noise reduction, and better understanding of open quantum dynamics.