Non-Markovian Quantum Process Tomography

Characterization protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This trajectory is expected to continue in building the next generation of devices - ones that can surpass classical computers for particular tasks - but progress in characterization must keep up with the complexities of intricate device noise. A missing piece in the zoo of characterization procedures is tomography, which can completely describe non-Markovian dynamics over a given time frame. Here, we formally introduce a generalization of quantum process tomography, which we call process tensor tomography. We detail the experimental requirements, construct the necessary postprocessing algorithms for maximum-likelihood estimation, outline the best-practice aspects for accurate results, and make the procedure efficient for low-memory processes. The characterization is a pathway to diagnostics and informed control of correlated noise. As an example application of the hardware-agnostic technique, we show how its predictive control can be used to substantially improve multitime circuit fidelities on superconducting quantum devices. Our methods could form the core for carefully developed software that may help hardware consistently pass the fault-tolerant noise threshold.