Demonstration of non-Markovian process characterisation and control on a quantum processor

As experimentally available quantum devices increase in precision and accessibility, attention is turning to understanding and eliminating correlated -- or non-Markovian -- noise. Here, we develop and experimentally test a generalisation of quantum process tomography specifically for this problem. Based on the process tensor, this framework is designed to characterise non-Markovian dynamics in quantum systems by measuring the system’s response to a basis of control operations. The method was demonstrated on an array IBM Quantum devices where the effects of any control operation in the span were discernible to an infidelity of 10^-3. We discuss the subtleties and best practices for the approach, and also demonstrate several applications: a statistically significant lower-bound on memory size for quantum devices; high fidelity dynamical characterisation in situations where conventional Markov models appreciably break down; and finally, demonstrate how the characterisation can be used for optimal local control of a system and its non-Markovian bath. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation and noise reduction.