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Optical and Quantum Sensing and Precision Metrology II

Quantum control of Dicke states

Vladimir S. Malinovsky, Sebastián Carrasco, Vladan Vuletić

Published Mar 8, 2023• 0 citations
Publisher
DOI
10.1117/12.2657373

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We explore the feasibility of realizing Dicke states in qubit arrays with always-on isotropic Heisenberg coupling between adjacent qubits, assuming a single Zeeman-type control acting in the zzz direction on an actuator qubit. The Lie-algebraic criteria of controllability imply that such an array is not completely controllable, but satisfies the conditions for subspace controllability on any subspace with a fixed number of excitations. Therefore, a qubit array described by the model under consideration is state-to-state controllable for an arbitrary choice of initial and final states that have the same Hamming weight. This limited controllability is exploited here for the time-efficient dynamical generation of an aaa-excitation Dicke state ∣DaN⟩|D^{N}_{a}\rangle∣DaN​⟩ (a=1,2,…,N−1a=1,2,\ldots, N-1a=1,2,…,N−1) in a linear array with NNN qubits starting from a generic Hamming-weight-aaa product state. To dynamically generate the desired Dicke states -- including WWW states ∣WN⟩|W_{N}\rangle∣WN​⟩ as their special (a=1a=1a=1) case -- in the shortest possible time with a single local ZZZ control, we employ an optimal-control scheme based on the {\em dressed chopped random basis} (dCRAB) algorithm. We optimize the target-state fidelity over the expansion coefficients of smoothly-varying control fields in a truncated random Fourier basis; this is done by combining Nelder-Mead-type local optimizations with the multistart-based clustering algorithm that facilitates searches for global extrema. In this manner, we obtain the optimal control fields for Dicke-state preparation in arrays with up to 999 qubits. Based on our numerical results, we find that the shortest possible state-preparation times scale as O(N2.08)\mathcal{O}(N^{2.08})O(N2.08) for WWW states and O(N1.78)\mathcal{O}(N^{1.78})O(N1.78) for a=2a=2a=2 Dicke states.