The development of practical quantum processors relies on the ability to control and predict their functioning despite the presence of noise. This is particularly challenging for temporarily correlated noise. Here we propose a physics-inspired supervised machine learning approach to efficiently and accurately predict the functioning of quantum processors in the presence of correlated noise, which only requires data from randomized benchmarking experiments. To demonstrate the efficacy of our technique, we analyze the data from a superconducting quantum processor with tunable correlated noise. We produce training data by evolving the system for a number of time steps, and with this, we fully quantify the correlated noise and accurately predict the dynamics of the system for times beyond the training data. This approach shows a path towards efficient and effective learning of noisy quantum dynamics and optimally control quantum processors over long and complex computations even in the presence of correlated noise.
