Modelling non-markovian quantum processes with recurrent neural networks

Quantum systems interactingwith an unknown environment are notoriously difficult tomodel, especially in presence of non-Markovian and non-perturbative effects. Herewe introduce a neural network based approach,which has the mathematical simplicity of theGorini–Kossakowski–Sudarshan–Lindblad master equation, but is able tomodel non-Markovian effects in different regimes. This is achieved by using recurrent neural networks(RNNs)for defining Lindblad operators that cankeep track of memory effects. Building upon thisframework,we also introduce a neural network architecture that is able to reproduce the entire quantum evolution, given an initial state. As an application we study how to train these modelsfor quantum process tomography, showing that RNNs are accurate over different times and regimes.