  Although single and two-qubit gates are sufficient for universal quantum
computation, single-shot three-qubit gates greatly simplify quantum error
correction schemes and algorithms. We design fast, high-fidelity three-qubit
entangling gates based on microwave pulses for transmon qubits coupled through
a superconducting resonator. We show that when interqubit frequency differences
are comparable to single-qubit anharmonicities, errors occur primarily through
a single unwanted transition. This feature enables the design of fast
three-qubit gates based on simple analytical pulse shapes that are engineered
to minimize such errors. We show that a three-qubit ccz gate can be performed
in 260 ns with fidelities exceeding $99.38\%$, or $99.99\%$ with numerical
optimization.
