Frequency- and Amplitude- Modulated Pulses for Single- and Two-Qubit Gates*

To achieve lower error rates in superconducting qubits, more robust quantum control is becoming increasingly important. We introduce a method of pulse design for single- and two-qubit gates using optimal quantum control schemes in an extended Hilbert space leveraging Floquet theory. In contrast to more traditional pulse design focused solely on amplitude modulation of the pulse envelope, we concentrate on deliberately manipulating both the amplitude and frequency of the pulse with the goal of achieving faster gates while maintaining the robustness and fidelity. We present numerical simulations using our method and progress towards realizing robust high-fidelity gates using the frequency-modulated pulses.