The hybrid quantum system in which interactions between superconducting (SC) qubits and atomic qubits are mediated by an auxiliary cavity mode is a promising architecture for quantum information processing. However, compared to the strong coupling g1 between the SC qubits and the cavity, the coupling g2 between the atomic qubits and the cavity is often extremely weak, which limits the operation speed and suffers more from dissipations. Here we propose a built-in fault-tolerant geometric operation to speed up the generation of entanglement between SC qubits and atomic qubits only by linearly driving the qubits. The operation speed is proportional to g1g2 instead of the weaker coupling g2. Comparing with traditional double-swap method, the speedup can reach around 10 times and the fidelity keeps high under current experimental parameters. This speedup technique can be used in various boson-mediated quantum platforms even if parametric driving or modulation of the boson mode is impossible, enabling exploration of fast quantum information processing.
The geometric phase (GP) of a periodically driven symmetricspin-boson model (SBM) is investigated using the process-tensor time-evolving matrix product operator (PT-TEMPO) method. A longitudinal monochromatic field drives the qubit along the \emph{same} coordinate that couples to an Ohmic bosonic environment. The gauge-invariant kinematic GP is evaluated from the reduced-statetrajectory, and a circular non-additivity measure quantifies the combined effects of driving and dissipation relative to driven-unitary and undriven-dissipative references. Amplitude, frequency, coupling-strength, and bath-cutoff sweeps reveal regimes in which periodic driving reduces or enhances environmental phase deformation relative to the unitary counterpart. The one-cycle GP exhibits pronounced nonmonotonic drive frequency dependence, while its bath-induced shift depends sensitively on both coupling strength and cutoff. These trends are interpreted qualitatively in terms of Floquet dressing and bath spectral structure. A two-cycle echo provides a complementary reversibility diagnostic, whose persistence signal does not generally measure the Tong GP. The results characterize the non-additive influence of driving and dissipation on geometric-phase dynamics and identify parameter regimes of reduced bath-induced deformation.