Quantum information processing with superconducting circuits: a review

During the last ten years, superconducting circuits and systems have passed from interesting physical devices to contenders for useful information processing in the near future. There are now advanced simulation experiments with nine qubits, and commitments to demonstrate quantum supremacy with fifty qubits within just a few years. The time is therefore ripe for providing an overview of superconducting devices and systems: to discuss the state of the art of applications to quantum information processing (QIP), and to describe recent and upcoming applications of superconducting systems to digital and analogue computing and simulation in Physics and Chemistry. On top of that, the review will try to address general questions like „What can a quantum computer do that a classical computer can’t?“.