We present a unified scheme for generating high-fidelity entangling gates in superconducting platforms by continuous dynamical decoupling (CDD) combined with variational minimal-energy optimal control. During the CDD stage, we suppress residual couplings, calibration drifting, and quasistatic noise, resulting in a stable effective Hamiltonian that preserves an interaction proportional to ZZ and YY coupling terms, necessary for generating entanglement. In this stable $\mathrm{SU}\left(4\right)$ manifold, we calculate smooth low-energy single-quibt control functions using a variational geodesic optimization process that directly minimizes gate infidelity. We illustrate the methodology by applying it to CZ, CX, and a two-qubit gate constructed as a CX followed by random single-qubit rotations, achieving virtually unit fidelity and robustness under restricted single-qubit action, with experimentally realistic control fields. These results establish CDD-enhanced variational geometric optimal control as a practical and noise-resilient scheme for designing superconducting entangling gates.

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• Open quantum systems & decoherence
• Quantum computation
• Quantum control
• Quantum gates
• Qubits