Efficient preparation of Dicke states

We present an algorithm utilizing mid-circuit measurement and feedback that prepares Dicke states with polylogarithmically many ancillas and polylogarithmic depth. Our algorithm uses only global mid-circuit projective measurements and adaptively-chosen global rotations. This improves over prior work that was only efficient for Dicke states of low weight, or was not efficient in both depth and width. Our algorithm can also naturally be implemented in a cavity QED context using polylogarithmic time, zero ancillas, and atom-photon coupling scaling with the square root of the system size.