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Abstract

Quantum technologies hold the promise to revolutionise our society with
ground-breaking applications in secure communication, high-performance
computing and ultra-precise sensing. One of the main features in scaling up
quantum technologies is that the complexity of quantum systems scales
exponentially with their size. This poses severe challenges in the efficient
calibration, benchmarking and validation of quantum states and their dynamical
control. While the complete simulation of large-scale quantum systems may only
be possible with a quantum computer, classical characterisation and
optimisation methods (supported by cutting edge numerical techniques) can still
play an important role.
Here, we review classical approaches to learning quantum systems, their
correlation properties, their dynamics and their interaction with the
environment. We discuss theoretical proposals and successful implementations in
different physical platforms such as spin qubits, trapped ions, photonic and
atomic systems, and superconducting circuits. This review provides a brief
background for key concepts recurring across many of these approaches, such as
the Bayesian formalism or Neural Networks, and outlines open questions.