  A quantum computer will use the properties of quantum physics to solve
certain computational problems much faster than otherwise possible. One
promising potential implementation is to use superconducting quantum bits in
the circuit quantum electrodynamics (cQED) architecture. There, the low energy
states of a nonlinear electronic oscillator are isolated and addressed as a
qubit. These qubits are capacitively coupled to the modes of a
microwave-frequency transmission line resonator which serves as a quantum
communication bus. Microwave electrical pulses are applied to the resonator to
manipulate or measure the qubit state. State control is calibrated using
diagnostic sequences that expose systematic errors. Hybridization of the
resonator with the qubit gives it a nonlinear response when driven strongly,
useful for amplifying the measurement signal to enhance accuracy. Qubits
coupled to the same bus may coherently interact with one another via the
exchange of virtual photons. A two-qubit conditional phase gate mediated by
this interaction can deterministically entangle its targets, and is used to
generate two-qubit Bell states and three-qubit GHZ states. These three-qubit
states are of particular interest because they redundantly encode quantum
information. They are the basis of the quantum repetition code prototypical of
more sophisticated schemes required for quantum computation. Using a
three-qubit Toffoli gate, this code is demonstrated to autonomously correct
either bit- or phase-flip errors. Despite observing the expected behavior, the
overall fidelity is low because of decoherence. A superior implementation of
cQED replaces the transmission-line resonator with a three-dimensional box
mode, increasing lifetimes by an order of magnitude. In-situ qubit frequency
control is enabled with control lines, which are used to fully characterize and
control the system Hamiltonian.
