  We have embedded two fixed-frequency Al/AlO$_{\textrm{x}}$/Al transmons, with
ground-to-excited transition frequencies at 6.0714 GHz and 6.7543 GHz, in a
single 3D Al cavity with a fundamental mode at 7.7463 GHz. Strong coupling
between the cavity and each transmon results in an effective qubit-qubit
coupling strength of 26 MHz and a -1 MHz dispersive shift in each qubit's
transition frequency, depending on the state of the other qubit. Using the
all-microwave SWIPHT (Speeding up Waveforms by Inducing Phases to Harmful
Transitions) technique, we demonstrate the operation of a generalized
controlled-not (CNOT) gate between the two qubits, with a gate time $\tau_g=
907$ ns optimized for this device. Using quantum process tomography we find
that the gate fidelity is 83%-84%, somewhat less than the 87% fidelity expected
from relaxation and dephasing in the transmons during the gate time.
