Robust CZ gate against flux line memory

High-fidelity CZ gates are central to superconducting quantum processors, but flux line distortion complicates the reuse of calibrated gate pulses. Continuous predistortion can compensate for pulse history by updating the input across gate boundaries, provided that the line model and initialization are accurate. To enable reliable reuse of fixed, gate-local predistorted CZ pulses without continuous compensation and reduce sensitivity to an uncertain initial line state, we model flux line distortion as the dynamics of a stateful classical actuator coupled to a quantum system. Using a first-order Dyson expansion, we derive the error generators induced by variations in the initial flux-line state. We then design a robust CZ gate by optimizing the flux pulse to suppress these generators and minimize the residual flux line state at the gate exit. In a one-pole flux line model, the optimized CZ pulse exhibits the expected first-order robustness plateau and, over ten consecutive gates, maintains high fidelity across a broader initial state range than continuous predistortion initialized at zero. For a more practical three-pole model, the optimized CZ pulse achieves F_avg = 99.998% in closed-system simulations, suppresses all first-order error generators, and brings the residual flux close to zero. Reusing the fixed, gate-local predistorted pulse without additional waiting between gates yields F_avg = 99.97% over ten gates and reduces infidelity by approximately 2.3×10³ relative to the baseline under the same predistortion method. These results show that explicitly accounting for flux line memory enables high-fidelity reuse of fixed, gate-local predistorted CZ pulses across repeated gate sequences.