pulses, preventing the precise closure of cyclic evolution. This mechanism renders conventional symmetric protocols intrinsically over-constrained. Conventional strategies typically rely on smoothing the pulse envelopes or embedding the interaction pulse within a longer qubit pulse to bypass short-timescale distortions, which inevitably leads to a persistent speed-fidelity trade-off. To overcome this limitation, we introduce a cyclic control strategy based on parameter-space expansion, which restores controllability by incorporating an additional degree of freedom. We experimentally demonstrate this approach in a superconducting controlled-Z gate, achieving robust suppression of coherent errors without increasing gate duration, reducing the average coherent error from 0.27% to 0.12% across multiple two-qubit gates, as validated by cross-entropy benchmarking. Our results establish a general route to fast, high-fidelity cyclic quantum gates beyond the conventional speed-fidelity trade-off.

The method appends a reset segment with tailored amplitude and phase to a normal square readout pulse. Within the linear-response regime, the optimal reset amplitude scales proportionally with the readout amplitude, while the optimal reset phase remains nearly invariant, significantly simplifying the calibration process. By characterizing the cavity photons dynamics, we show that the SSPE pulse accelerates photon depletion by up to a factor of six compared to passive free decay. We further quantify the qubit backaction induced by the readout pulse and find that the SSPE pulse yields the lowest excitation and relaxation rates compared to a Square and CLEAR pulses. Our results establish the SSPE scheme as a practical and scalable approach for achieving fast, smooth, low-backaction cavity reset in superconducting quantum circuits.