High-fidelity and robust quantum gate is a prerequisite for realizing practical quantum computing. Our control method by designing the optimized control pulses can effectively reduce the gate infidelity over an order of magnitude and also enlarge the robust windows against the noise and the system parameter uncertainty as compared to the experimental method for the quantum-dot spin qubits. We will apply this technique on the realistic devices to experimentally realize the high-fidelity and robust quantum gates and will also extend this technique to multi-qubit gate control, paving the way for large-scale fault-tolerant quantum computing.

     Because of their long coherence time and compatibility with industrial foundry processes, electron spin qubits are a promising platform for scalable quantum processors. A full-fledged quantum computer will need quantum error correction, which requires high-fidelity quantum gates. Analyzing and mitigating gate errors are useful to improve gate fidelity. Here, we demonstrate a simple yet reliable calibration procedure for a high-fidelity controlled-rotation gate in an exchange-always-on Silicon quantum processor, allowing operation above the fault-tolerance threshold of quantum error correction. We find that the fidelity of our uncalibrated controlled-rotation gate is limited by coherent errors in the form of controlled phases and present a method to measure and correct these phase errors. We then verify the improvement in our gate fidelities by randomized benchmark and gateset tomography protocols. Finally, we use our phase correction protocol to implement a virtual, high-fidelity, controlled-phase gate.