Quantum measurement in action with the transmon qubit

High fidelity, rapid quantum non-demolition readout of superconducting qubits greatly facilitates tests of single qubit measurement theory. We have realized such readout in an experiment comprised of a transmon coupled to a compact resonator, which is in turn connected via an isolator and circulator to a tunable Josephson parametric converter (JPC) operated as a phase-preserving parametric amplifier. When the qubit state is measured with an rf tone corresponding to an average cavity circulating power of 5 photons, fidelity exceeds 90{\%} for a measurement duration of 240 ns ($\sim $0.1 T1). This performance allows the observation of quantum trajectories of the qubit, showing discrete jumps and a bimodal distribution of measurement results, despite the linear character of the amplifier. This provides further support for the quantum nature of superconducting artificial atoms. We have conducted Stern-Gerlach type experiments, in which the qubit is repeatedly measured along different axes. Results are in good agreement with theoretical predictions of the effect of partial measurement on qubit state evolution.