Robust generation of a magnonic cat state via a superconducting flux qubit

We study the hybrid system of a high-quality yttrium-iron-garnet (YIG) sphere magnetically coupled to a superconducting flux qubit via the magnetic fields created by two persistent-current quantum states. When the flux qubit is operated away from its sweet point, a coherent nonlinear two-magnon interaction can be predicted; that is, the qubit is excited by absorbing a pair of magnons. We show that the spontaneous emission of the qubit can be exploited to steer the magnon mode of the YIG sphere into a Schrödinger cat state with high fidelity. Our scheme has practical advantages in that it eliminates the need for precise control of the evolution time and the projective measurement, and is also insensitive to the qubit's pure dephasing.