Efficient detection of inhomogeneous magnetic fields from a single spin with Dicke states

Preparing Dicke states in a spin ensemble using phase estimation

“…The jth round phase estimation for the unitary operator U = e i2π Jz /2 K in Eq. (7). This circuit projectively measures the eigenvalues of the unitary operator U j = e iπ 2 1− j (Jz −A j−1 ) on the input state |ψ j−1 in Eq.…”

“…N-qubit Dicke states form a class of entangled states which are interesting for metrology [6][7][8][9][10]. Compared to other states used in quantum sensing, Dicke states have been argued to be more robust to various noise sources such as spin dephasing, spin damping, and spin number fluctuations [9].…”

“…Compared to other states used in quantum sensing, Dicke states have been argued to be more robust to various noise sources such as spin dephasing, spin damping, and spin number fluctuations [9]. Recent work has demonstrated a scheme to use Dicke states for detecting the magnetic field induced by a single spin [7]. Another distinctive feature of the use of Dicke states is that the optimal sensitivity can be obtained through only global control on the set of spins [9,10].…”

“…This limitation excludes quantum algorithms for preparing Dicke states which are based on the full addressability of the qubits [25,26]. To address this issue, some work has been dedicated to schemes which require only a global control of the spin ensemble, such as using steadystate evolution [27], repeated energy transfer [7], continuous weak measurements [28], and the use of geometric phase gates [29]. Unfortunately, these methods are still demanding currently when N is large, as they often need complicated measurement-based feedback, high fidelity control, and long preparation times.…”

“…For example, the optimized scheme in Ref. [7] uses O(N ) rounds of initialization and evolution of an ancilla qubit. Our goal is to improve the scaling with N so that one could possibly handle a larger error rate on the ancilla qubit.…”