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 $T_ϕ$, thereby quantifying the tradeoff between them. For fluxonium qubits with realistic noise spectra, our method enhances $T_ϕ$ 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.

💡 Research Summary

This paper addresses the fundamental limits and practical optimization of coherence in superconducting fluxonium qubits operated at dynamical sweet spots (DSSs). The authors first generalize the notion of a DSS beyond the conventional single‑tone or two‑tone flux drives by allowing an arbitrary periodic flux modulation ϕ_ext(t)=ϕ_dc+ϕ_ac P(t), where P(t) is expressed as a Fourier series with complex coefficients p_n that are treated as free design parameters. Using Floquet theory, the time‑periodic Hamiltonian is mapped onto an infinite‑dimensional Floquet matrix, which is truncated for numerical diagonalization. The resulting quasienergies and Floquet states provide a complete description of the driven qubit’s dynamics and its coupling to environmental noise.

The noise model incorporates both 1/f flux noise and dielectric loss, yielding a spectral density S(ω)=A_f²/(2π|ω|)+κ(ω,T)A_d²ℏ|ω|/(2π). By projecting the system‑bath interaction σ_z β onto the Floquet basis, the authors derive analytic expressions for the pure dephasing rate γ_z and the energy‑relaxation rates γ_± in terms of the Fourier components g