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.
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