Cavity magnonics with domain walls in insulating ferromagnetic wires

Magnetic domain walls (DWs) are topological defects that host robust low-energy modes, which can be harnessed for classical and neuromorphic computing. However, accessing their quantum dynamics has remained an outstanding challenge. Using concepts from cavity optomechanics, we show that a geometric, Coriolis-type interaction between localized DWs and extended magnon modes in short insulating ferromagnetic wires enables efficient cooling of DWs to their quantum ground state and the preparation of nonclassical states with negative Wigner functions, detectable in the power spectrum of emitted magnons. We further demonstrate that magnons can mediate long-range entangling interactions between qubits encoded in spatially separated DWs, providing a route toward universal quantum gate operations. Our proposal relies solely on intrinsic degrees of freedom of the ferromagnet and naturally extends to ferrimagnets and antiferromagnets, as well as to other confined magnetic textures such as vortices and skyrmions in insulating nanostructures.