## Nonlinear response of the vacuum Rabi resonance

On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By using a cavity to confine the field, the strength of this interaction can be increased by many orders of magnitude, to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics has been reached for real atoms in optical cavities, and for artificial atoms in circuit quantum electrodynamics and quantum dot systems.

## Proposal for generating and detecting multi-qubit GHZ states in circuit QED

We propose methods for the preparation and entanglement detection of multi-qubit Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum electrodynamics. Using quantum trajectory simulations appropriate for the situation of a weak continuous measurement, we show that the joint dispersive readout of several qubits can be utilized for the probabilistic production of high-fidelity GHZ states. When employing a nonlinear filter on the recorded homodyne signal, the selected states are found to exhibit values of the Bell–Mermin operator exceeding 2 under realistic conditions.

## Randomized benchmarking and process tomography for gate errors in a solid-state qubit

We present measurements of single-qubit gate errors for a superconducting qubit. Results from quantum process tomography and randomized benchmarking are compared with gate errors obtained from a double π pulse experiment. Randomized benchmarking reveals a minimum average gate error of 1.1±0.3% and a simple exponential dependence of fidelity on the number of gates. It shows that the limits on gate fidelity are primarily imposed by qubit decoherence, in agreement with theory.

## Controlling the Spontaneous Emission of a Superconducting Transmon Qubit

We present a detailed characterization of coherence in seven transmon qubits in a circuit QED architecture. We find that spontaneous emission rates are strongly influenced by far off-resonant modes of the cavity and can be understood within a semiclassical circuit model. A careful analysis of the spontaneous qubit decay into a microwave transmission-line cavity can accurately predict the qubit lifetimes over two orders of magnitude in time and more than an octave in frequency. Coherence times T1 and T2* of more than a microsecond are reproducibly demonstrated.

## Suppressing charge noise decoherence in superconducting charge qubits

We present an experimental realization of the transmon qubit, an improved superconducting charge qubit derived from the Cooper pair box. We experimentally verify the predicted exponential suppression of sensitivity to 1/f charge noise [J. Koch et al., Phys. Rev. A 76, 042319 (2007)]. This removes the leading source of dephasing in charge qubits, resulting in homogenously broadened transitions with relaxation and dephasing times in the microsecond range.