  We propose a theoretical protocol to implement multiqubit geometric gates
(i.e., the M{\o}lmer-S{\o}rensen gate) using photonic cat-state qubits. These
cat-state qubits stored in high-$Q$ resonators are promising for
hardware-efficient universal quantum computing. Specifically, in the limit of
strong two-photon drivings, phase-flip errors of the cat-state qubits are
effectively suppressed, leaving only a bit-flip error to be corrected. Because
this dominant error commutes with the evolution operator, our protocol
preserves the error bias, and, thus, can lower the code-capacity threshold for
error correction. A geometric evolution guarantees the robustness of the
protocol against stochastic noise along the evolution path. Moreover, by
changing detunings of the cavity-cavity couplings at a proper time, the
protocol can be robust against parameter imperfections (e.g., the total
evolution time) without introducing extra noises into the system. As a result,
the gate can produce multi-mode entangled cat states in a short time with high
fidelities.
