Pareto-Front Engineering of Dynamical Sweet Spots in Superconducting Qubits

Operating superconducting qubits at dynamical sweet spots (DSSs) suppresses decoherence from low-frequency flux noise. A key open question is how long coherence can be extended under this strategy and what fundamental limits constrain it. Here we introduce a fully parameterized, multi-objective periodic-flux modulation framework that simultaneously optimizes energy relaxation $T_1$ and pure dephasing $T_\phi$, thereby quantifying the tradeoff between them. For fluxonium qubits with realistic noise spectra, our method enhances $T_\phi$ by a factor of 3-5 compared with existing DSS strategies while maintaining $T_1$ in the hundred-microsecond range. We further prove that, although DSSs eliminate first-order sensitivity to low-frequency noise, relaxation rate cannot be reduced arbitrarily close to zero, establishing an upper bound on achievable $T_1$. At the optimized working points, we identify double-DSS regions that are insensitive to both DC and AC flux, providing robust operating bands for experiments. As applications, we design single- and two-qubit control protocols at these operating points and numerically demonstrate high-fidelity gate operations. These results establish a general and useful framework for Pareto-front engineering of DSSs that substantially improves coherence and gate performance in superconducting qubits.