  We introduce a strategy to develop optimally designed fields for continuous
dynamical decoupling (CDD). Our methodology obtains the optimal continuous
field configuration to maximize the fidelity of a general one-qubit quantum
gate. To achieve this, considering dephasing-noise perturbations, we employ an
auxiliary qubit instead of the boson bath to implement a purification scheme,
which results in unitary dynamics. Employing the sub-Riemannian geometry
framework for the two-qubit unitary group, we derive and numerically solve the
geodesic equations, obtaining the optimal time-dependent control Hamiltonian.
Also, due to the extended time required to find solutions to the geodesic
equations, we train a neural network on a subset of geodesic solutions,
enabling us to promptly generate the time-dependent control Hamiltonian for any
desired gate, which is crucial in circuit optimization.
