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 T1 and pure dephasing Tϕ, thereby quantifying the tradeoff between them. For fluxonium qubits with realistic noise spectra, our method enhances Tϕ by a factor of 3-5 compared with existing DSS strategies while maintaining T1 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 T1. As applications, we design leakage-suppressed single- and two-qubit control protocols at the optimized operating points and numerically demonstrate high-fidelity gates. These results establish a general and useful framework for Pareto-front engineering of DSSs that substantially improves coherence and gate performance in superconducting qubits. Noise limits how long superconducting qubits can store quantum information, a central challenge for reliable quantum computing. Here, they optimize generalized periodic flux modulation to find dynamical sweet spots in fluxonium qubits, improving dephasing times by 3-5 times while maintaining long relaxation times and enabling high-fidelity gates.