  We develop schemes for designing pulses that implement fast and precise
entangling quantum gates in superconducting qubit systems despite the presence
of nearby harmful transitions. Our approach is based on purposely involving the
nearest harmful transition in the quantum evolution instead of trying to avoid
it. Using analytical tools, we design simple microwave control fields that
implement maximally entangling gates with fidelities exceeding 99% in times as
low as 40 ns. We demonstrate our approach in a two-qubit circuit QED system by
designing the two most important quantum entangling gates: a conditional-NOT
gate and a conditional-Z gate. Our results constitute an important step toward
overcoming the problem of spectral crowding, one of the primary challenges in
controlling multi-qubit systems.
