We report the characterization of a two-qubit processor implemented with two
capacitively coupled tunable superconducting qubits of the transmon type, each
qubit having its own non-destructive single-shot readout. The fixed capacitive
coupling yields the \sqrt{iSWAP} two-qubit gate for a suitable interaction
time. We reconstruct by state tomography the coherent dynamics of the two-bit
register as a function of the interaction time, observe a violation of the Bell
inequality by 22 standard deviations after correcting readout errors, and
measure by quantum process tomography a gate fidelity of 90%