We report the realization of quantum microwave circuits using hybrid superconductor-semiconductor Josephson elements comprised of InAs nanowires contacted by NbTiN. Capacitively shunted single elements behave as transmon circuits with electrically tunable transition frequencies. Two-element circuits also exhibit transmonlike behavior near zero applied flux but behave as flux qubits at half the flux quantum, where nonsinusoidal current-phase relations in the elements produce a double-well Josephson potential. These hybrid Josephson elements are promising for applications requiring microwave superconducting circuits operating in a magnetic field. DOI: 10.1103/PhysRevLett.115.127002 PACS numbers: 85.25.Hv, 62.23.Hj, 74.45.+c, 84.40.Dc In superconducting circuits, macroscopic degrees of freedom like currents and voltages can exhibit quantum mechanical behavior. These circuits can behave as artificial atoms with discrete, anharmonic levels whose transitions can be driven coherently [1]. In the field of circuit quantum electrodynamics (cQED), these artificial atoms are coupled to resonators to perform microwave quantum optics in the solid state [2,3]. Over the past decade, cQED has also grown into a promising platform for quantum information processing, wherein the ground and first-excited levels of each atom serve as an effective qubit [4]. To date, implementations of superconducting quantum circuits have relied almost exclusively on aluminum-aluminum-oxidealuminum (Al=AlOx=Al) tunnel junctions as the source of nonlinearity without dissipation. However, many exciting applications require magnetic fields (∼0.5 T) at which superconductivity in aluminum is destroyed, calling for an alternative approach to realizing microwave artificial atoms.Recent advances in materials development and nanowire (NW) growth have enabled the development of superconductor-semiconductor structures supporting coherent charge transport without dissipation [5] and providing signatures of Majorana bound states [6]. To date, superconductor-semiconductor-superconductor Josephson elements (JEs) have been studied exclusively in quasi-dc [7][8][9][10] and radio-frequency [11] transport. Building microwave circuits operating in the quantum regime, in which transition energies between levels exceed the thermal energy, offers new ways to investigate the physics of hybrid superconductor-semiconductor structures using spectroscopy [12][13][14][15].In this Letter, we report the realization of microwavefrequency cQED circuits made from hybrid JEs based on InAs NWs contacted by NbTiN. Capacitively shunted single JEs behave as weakly anharmonic oscillators, or transmons [16], with transition frequencies tunable by the field effect, i.e., voltage on a proximal side gate. Doubleelement devices show similar transmonlike behavior at zero applied flux but behave as flux qubits [17] near full frustration owing to a double-well Josephson potential arising from nonsinusoidal current-phase relations (CPR s). We observe microwave-driven transitions between states ...

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