We use machine learning techniques to design a 50 ns three-qubit flux-tunable controlled-controlled-phase gate with fidelity of >99.99% for nearest-neighbor coupled transmons in circuitquantum electrodynamics architectures. We explain our gate design procedure where we enforce realistic constraints, and analyze the new gate’s robustness under decoherence, distortion, and random noise. Our controlled-controlled-phase gate in combination with two single-qubit gates realizes a Toffoli gate which is widely used in quantum circuits, logic synthesis, quantum error correction, and quantum games.
We have embedded two fixed-frequency Al/AlOx/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 modeat 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 τ_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.