We present a Dicke state preparation scheme which uses global control of $N$ spin qubits: our scheme is based on the standard phase estimation algorithm, which estimates the eigenvalue of a unitary operator. The scheme prepares a Dicke state nondeterministically by collectively coupling the spins to an ancilla qubit via a $ZZ$ interaction, using $\lceil {log}_{2}N\rceil +1$ ancilla qubit measurements. The preparation of such Dicke states can be useful if the spins in the ensemble are used for magnetic sensing: we discuss a possible realization using an ensemble of electronic spins located at diamond nitrogen-vacancy centers coupled to a single superconducting flux qubit. We also analyze the effect of noise and limitations in our scheme.

• Received 8 June 2021
• Accepted 20 August 2021

DOI:https://doi.org/10.1103/PhysRevA.104.032407