Robustness level sets for parametric quantum gate synthesis

A robust pulse is traditionally obtained by optimizing the fidelity of one target gate at a time, each gate on its own landscape, so a robust gate family appears only as a sequence of separately optimized pulses. Here we define a target-independent quantum control robustness landscape (QCRL) from the Magnus expansion of the noise propagator in the toggling frame. Robust controls of every gate in a parametric family lie on the same zero set of this landscape, at regular points a smooth local branch of dimension p − r for p control parameters and r independent constraints, and traversing it produces the family: robustness-invariant pulse variation (RIPV), the predictor–corrector continuation we use, varies one optimized seed pulse along the branch at a constraint residual of 10−10. For Rx(θ) under quasistatic dephasing one branch spans the full family at first and at first-plus-second order, with exact-propagation fidelity above 0.999 for every pulse up to relative detunings of 4.7% and 10.5%; the same construction yields a dual-control family robust to three-axis noise. By shifting from optimizing target-dependent fidelity to maintaining target-independent robustness, we unify the synthesis of robust gate families into a single geometric traversal.