Quantum superconducting circuits are presently the most successful solid state devices for quantum information processing. Recently, a new generation of Josephson elements has been developed based on semiconducting nanowires and carbon nanotubes. A novel type of superconducting qubit will be discussed in the talk, based on Andreev quantization in mesoscopic Josephson contacts. Such contacts present a sort of artificial atoms with sets of discrete levels, strong coupling of which to the Josephson current provides access to the levels both for the manipulation and measurement. We discuss the ways of manipulating and measuring the Andreev states in quantum point contacts with non-magnetic, and magnetic scatterers.

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