High-derivative DRAG for error reduction in single-qubit gates

To overcome the challenges posed by the finite coherence time of quantum systems, an important task is devising rapid and precise control schemes. For superconducting qubits, analytical control methods based on the system's Hamiltonian are often favoured over general numerical optimization for practical experimental implementation. We introduce an analytical control framework using multi-derivative pulse shaping, based on the Derivative Removal via Adiabatic Gate (DRAG) technique. This approach provides an efficient, parameterized pulse Ansatz that can simultaneously suppress multiple control errors, including nonperturbative effects and multi-photon dynamics.In this presentation, we show that multiple leakage channels are present in single-qubit gates when approaching the speed limit. By introducing high-derivative corrections, these errors can be systematically removed. We also show that a better understanding of the effective model reveals improved prediction of pulse parameters, significantly simplifying the experimental calibration procedure. We derive and optimize different DRAG pulses to minimize leakage and maximize the fidelity of single-qubit gates, demonstrating the need for pulses beyond the current standard for faster single-qubit gates.