  Quantum logic gates must perform properly when operating on their standard
input basis states, as well as when operating on complex superpositions of
these states. Experiments using superconducting qubits have validated the truth
table for particular implementations of e.g. the controlled-NOT gate [1,2], but
have not fully characterized gate operation for arbitrary superpositions of
input states. Here we demonstrate the use of quantum process tomography (QPT)
[3,4] to fully characterize the performance of a universal entangling gate
between two superconducting quantum bits. Process tomography permits complete
gate analysis, but requires precise preparation of arbitrary input states,
control over the subsequent qubit interaction, and simultaneous single-shot
measurement of the output states. We use QPT to measure the fidelity of the
entangling gate and to quantify the decoherence mechanisms affecting the gate
performance. In addition to demonstrating a promising fidelity, our entangling
gate has a on/off ratio of 300, a level of adjustable coupling that will become
a requirement for future high-fidelity devices. This is the first solid-state
demonstration of QPT in a two-qubit system, as solid-state process tomography
has previously only been demonstrated with single qubits [5,6].
