Nonadiabatic geometric quantum computation with cat qubits via invariant-based reverse engineering

We propose a protocol to realize nonadiabatic geometric quantum computation of small-amplitude Schr\"odinger cat qubits via invariant-based reverse engineering. We consider a system with a two-photon driven Kerr nonlinearity, which provides a pair of dressed even and odd coherent states, i.e., Schr\"odinger cat states for fault-tolerant quantum computations. An additional coherent field is applied to linearly drive a cavity mode, to induce oscillations between dressed cat states. By designing this linear drive with invariant-based reverse engineering, nonadiabatic geometric quantum computation with cat qubits can be implemented. The performance of the protocol is estimated by taking into account the influence of systematic errors, additive white Gaussian noise, and decoherence including photon loss and dephasing. Numerical results demonstrate that our protocol is robust against these negative factors. Therefore, this protocol may provide a feasible method for nonadiabatic geometric quantum computation in bosonic systems.