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This research demonstrates a time-efficient method to generate specific Dicke states, including W-states, in qubit arrays using only a single local control field via subspace controllability principles. By leveraging the dCRAB optimal-control algorithm, the study achieves state preparation times that scale quadratically with system size for key entangled states, offering practical advantages for scalable quantum hardware design.
Harnessing subspace controllability: Dynamical generation of Dicke states in Heisenberg-coupled qubit arrays with a single local control
arXiv:2512.24406v4 Announce Type: replace Abstract: 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 $z$ 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 $a$-excitation Dicke state $|D^{N}_{a}\rangle$ ($a=1,2,\ldots, N-1$) in a linear array with $N$ qubits starting from a generic Hamming-weight-$a$ product state. To dynamically generate the desired Dicke states -- including $W$ states $|W_{N}\rangle$ as their special ($a=1$) case -- in the shortest possible time with a single local $Z$ 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 $9$ qubits. Based on our numerical results, we find that the shortest possible state-preparation times scale as $\mathcal{O}(N^{2.08})$ for $W$ states and $\mathcal{O}(N^{1.78})$ for $a=2$ Dicke states.
Abstract: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 $z$ 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 $a$-excitation Dicke state $|D^{N}_{a}\rangle$ ($a=1,2,\ldots, N-1$) in a linear array with $N$ qubits starting from a generic Hamming-weight-$a$ product state. To dynamically generate the desired Dicke states -- including $W$ states $|W_{N}\rangle$ as their special ($a=1$) case -- in the shortest possible time with a single local $Z$ 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 $9$ qubits. Based on our numerical results, we find that the shortest possible state-preparation times scale as $\mathcal{O}(N^{2.08})$ for $W$ states and $\mathcal{O}(N^{1.78})$ for $a=2$ Dicke states.
arXiv:2512.24406 [quant-ph]
(or arXiv:2512.24406v4 [quant-ph] for this version)
Phys. Rev. Research 8, 033095 (2026)
https://doi.org/10.1103/t2zk-4nxh DOI(s) linking to related resources
From: Vladimir Stojanovic M. [view email] [v1] Tue, 30 Dec 2025 18:38:11 UTC (234 KB) [v2] Mon, 30 Mar 2026 14:22:25 UTC (258 KB) [v3] Mon, 22 Jun 2026 17:31:02 UTC (400 KB) [v4] Thu, 23 Jul 2026 13:54:36 UTC (400 KB)
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