Effective Implementation Of Nonadiabatic Geometric Swap Gate And Fredkin Gate Of Cat‐State Qubits Using An Auxiliary Ququart

We propose a feasible approach to implement nonadiabatic geometric SWAP and Fredkin gates for cat‐state qubits using Kerr‐nonlinear resonators driven by two‐photon squeezing fields. By coupling an auxiliary ququart (a four‐level system) to the resonators, a resonator‐selective transition of the ququart is achieved through precise optical control. This selective transition enables conditional flipping of the states of target cat‐state qubits based on the state of control qubits, forming the basis for high‐fidelity multi‐qubit gate operations. Leveraging this mechanism, both SWAP and Fredkin gates are realized through a fixed operational sequence, with the number of steps remaining constant regardless of the number of involved cat‐state qubits. Numerical simulations confirm robust performance under realistic conditions, including parameter inaccuracies, imbalanced couplings, inter‐resonator crosstalk, and decoherence. Therefore, this approach offers a robust and practical method for implementing nonadiabatic geometric SWAP and Fredkin gates with cat‐state qubits.