  At its core, Quantum Mechanics is a theory developed to describe fundamental
observations in the spectroscopy of solids and gases. Despite these practical
roots, however, quantum theory is infamous for being highly counterintuitive,
largely due to its intrinsically probabilistic nature. Neural networks have
recently emerged as a powerful tool that can extract non-trivial correlations
in vast datasets. They routinely outperform state-of-the-art techniques in
language translation, medical diagnosis and image recognition. It remains to be
seen if neural networks can be trained to predict stochastic quantum evolution
without a priori specifying the rules of quantum theory. Here, we demonstrate
that a recurrent neural network can be trained in real time to infer the
individual quantum trajectories associated with the evolution of a
superconducting qubit under unitary evolution, decoherence and continuous
measurement from raw observations only. The network extracts the system
Hamiltonian, measurement operators and physical parameters. It is also able to
perform tomography of an unknown initial state without any prior calibration.
This method has potential to greatly simplify and enhance tasks in quantum
systems such as noise characterization, parameter estimation, feedback and
optimization of quantum control.
