Electromagnetic signals are always composed of photons, although in the circuit domain those signals are carried as voltages and currents on wires, and the discreteness of the photon's energy is usually not evident. However, by coupling a superconducting quantum bit (qubit) to signals on a microwave transmission line, it is possible to construct an integrated circuit in which the presence or absence of even a single photon can have a dramatic effect. Such a system can be described by circuit quantum electrodynamics (QED)-the circuit equivalent of cavity QED, where photons interact with atoms or quantum dots. Previously, circuit QED devices were shown to reach the resonant strong coupling regime, where a single qubit could absorb and re-emit a single photon many times. Here we report a circuit QED experiment in the strong dispersive limit, a new regime where a single photon has a large effect on the qubit without ever being absorbed. The hallmark of this strong dispersive regime is that the qubit transition energy can be resolved into a separate spectral line for each photon number state of the microwave field. The strength of each line is a measure of the probability of finding the corresponding photon number in the cavity. This effect is used to distinguish between coherent and thermal fields, and could be used to create a photon statistics analyser. As no photons are absorbed by this process, it should be possible to generate non-classical states of light by measurement and perform qubit-photon conditional logic, the basis of a logic bus for a quantum computer.

A new type of electrometer is described that uses a single-electron transistor (SET) and that allows large operating speeds and extremely high charge sensitivity. The SET readout was accomplished by measuring the damping of a 1.7-gigahertz resonant circuit in which the device is embedded, and in some ways is the electrostatic "dual" of the well-known radio-frequency superconducting quantum interference device. The device is more than two orders of magnitude faster than previous single-electron devices, with a constant gain from dc to greater than 100 megahertz. For a still-unoptimized device, a charge sensitivity of 1.2 x 10(-5) e/hertz was obtained at a frequency of 1.1 megahertz, which is about an order of magnitude better than a typical, 1/f-noise-limited SET, and corresponds to an energy sensitivity (in joules per hertz) of about 41 Planck's over 2pi.

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. Our systematic characterization of the qubit spectrum, anharmonicity, and charge dispersion shows excellent agreement with theory, rendering the transmon a promising qubit for future steps towards solid-state quantum information processing. PACS numbers: 03.67.Lx, 74.50.+r, Over the last decade, superconducting qubits have gained substantial interest as an attractive option for quantum information processing, cf. Refs. [1,2,3] for recent reviews. Although there already exist different realizations of superconducting qubits [4,5,6,7], all their coherence times are several orders of magnitude too short for large-scale quantum computation. Fortunately, an increase of coherence times from 2 ns in the first superconducting qubit [4] to microsecond times in present experiments [8,9,10,11] has already been shown, giving rise to hope that the remaining gap can be overcome by optimized quantum circuits and better materials. Coherence times can be either limited by dissipation (T 1 ) or dephasing (T * 2 ). Most superconducting qubits have dephasing times much shorter than the limit T * 2 = 2T 1 imposed by dissipation, because they are plagued by the influence of 1/f noise in charge, flux, or critical current. The transmon qubit is an improved design [12] derived from the original charge qubit [13] that renders it immune to its primary source of noise, 1/f charge noise, without making it more susceptible to either flux or critical current noise.The transmon consists of two superconducting islands connected by a Josephson tunnel junction. The tunneling of Cooper pairs between the two islands is governed by two energy scales: the charging energy E C and the Josephson energy E J . The transmon has a Hamiltonian identical to the Cooper pair box (CPB),wheren denotes the number of excess Cooper pairs on one of the islands and n g the offset charge due to the electrostatic environment. Because there are no dc connections to the qubit, n is integer-valued like an angular momentum, and the conjugate variableφ is a compact angle. Despite its basic CPB nature, the transmon is operated in a vastly different param-The primary benefit of this new regime is a suppression of the sensitivity to charge noise, which is exponential in the ratio E J /E C . The qubit spectrum becomes more uniformly spaced in the transmon, but it has been shown in [12] that the anharmonicity in the spectrum only decays as a weak alge-braic function of E J /E C , allowing it to be used as an effective two-level system. One of the reasons for the long coherence times of the design is that the state of the transmon q...

As low-loss non-linear elements, Josephson junctions are the building blocks of superconducting qubits. The interaction of the qubit degree of freedom with the quasiparticles tunneling through the junction represent an intrinsic relaxation mechanism. We develop a general theory for the qubit decay rate induced by quasiparticles, and we study its dependence on the magnetic flux used to tune the qubit properties in devices such as the phase and flux qubits, the split transmon, and the fluxonium. Our estimates for the decay rate apply to both thermal equilibrium and non-equilibrium quasiparticles. We propose measuring the rate in a split transmon to obtain information on the possible non-equilibrium quasiparticle distribution. We also derive expressions for the shift in qubit frequency in the presence of quasiparticles.