Enhancing quantum coherence of a fluxonium qubit by employing flux modulation with tunable-complex-amplitude

We propose to protect fluxonium qubits that are away from half flux quantum against environmental noises, especially 1 / f flux noise, by adopting a modulated flux with tunable-complex-amplitude. Using open-system Floquet theory, we derive a Lindblad equation and extract decoherent rates for pure-dephasing, excitation and relaxation. After examining intrinsic attributes of the flux driven fluxonium qubit, we put forward an analytic manner to locate dynamical sweet spots for fast and weak driving. Continuous families of dynamical sweet spots are found in the parameter plane of relative amplitude factor and relative phase. Around a family of dynamical sweet spots or between two families of dynamical sweet spots, there exist continuous regions with long coherent times that exceed 100 μ s . Taking advantage of the two noise-insensitive channels: relative amplitude factor and relative phase, a flux driven fluxonium qubit can become immune to flux noises from both the dc and ac flux amplitudes. And the optimal driving amplitudes are no longer isolated at a certain driving frequency, but become continuous. This is in sharp contrast to the usual schemes based on flux modulation with real-amplitude. As a result, there are plenty of manipulating flexibility in our flux driving scheme with tunable-complex-amplitude, which may be useful in logical operations among flux driven fluxonium qubits or other flux qubits.