Protecting superconducting qubits from low-frequency noise is essential for advancing superconducting quantum computation. Based on the application of a periodic drive field, we develop a protocol for engineering dynamical sweet spots which reduce the susceptibility of a qubit to low-frequency noise. Using the framework of Floquet theory, we prove rigorously that there are manifolds of dynamical sweet spots marked by extrema in the quasi-energy differences of the driven qubit. In particular, for the example of fluxonium biased slightly away from half a flux quantum, we predict an enhancement of pure-dephasing by three orders of magnitude. Employing the Floquet eigenstates as the computational basis, we show that high-fidelity single- and two-qubit gates can be implemented while maintaining dynamical sweet-spot operation. We further confirm that qubit readout can be performed by adiabatically mapping the Floquet states back to the static qubit states, and subsequently applying standard measurement techniques. Our work provides an intuitive tool to encode quantum information in robust, time-dependent states, and may be extended to alternative architectures for quantum information processing.
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