Machine-learning-based three-qubit gate design for the Toffoli gate and parity check in transmon systems

We use machine-learning techniques to design three-qubit entangling gates with fidelities of >99.9% and duration of 50 ns for nearest-neighbor coupled flux-tunable transmons in circuit quantum electrodynamics architectures. The gate design procedure enforces realistic constraints and analyzes the robustness of the new gates under decoherence, distortion, and random noise. The controlled-controlled-phase gate in combination with two single-qubit gates realizes a Toffoli gate which is widely used in quantum circuits, logic synthesis, and quantum error correction. We also introduce a three-qubit entangling Parity Checker gate which has applications in quantum arithmetic circuits and quantum error correction schemes. Using these three-qubit gates, we design a circuit for Shor's nine-qubit quantum error correction code and compare its performance to conventional realizations.