Preparing Dicke states in a spin ensemble using phase estimation

TL;DR

This paper introduces a method to prepare Dicke states in a spin ensemble using phase estimation and global control, which is useful for magnetic sensing applications with NV centers.

Contribution

The authors propose a non-deterministic Dicke state preparation scheme based on phase estimation with minimal ancilla qubits and analyze its feasibility and noise effects.

Findings

Scheme requires $ ext{O}(\log N)$ ancilla measurements.

Potential implementation with NV centers and superconducting qubits.

Noise analysis shows robustness under certain conditions.

Abstract

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 non-deterministically by collectively coupling the spins to an ancilla qubit via a $ZZ$-interaction, using $\ceil*{\log_2 N} + 1$ 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 (NV) centers coupled to a single superconducting flux qubit. We also analyze the effect of noise and limitations in our scheme.