Intelligent control of collisional architectures for multipartite Dicke-state preparation

Designing scalable, noise-tolerant control protocols for multipartite entanglement is a central challenge for quantum technologies, and it naturally calls for \emph{algorithmic} synthesis of interaction parameters rather than handcrafted gate sequences. Here we introduce an intelligent, constraint-aware control framework for deterministic generation of symmetric Dicke states $|D_n^{(m)}\rangle$ in repeated-interaction (collision-model) architectures. The protocol employs excitation-preserving partial-SWAP collisions between two disjoint qubit registers, mediated by $m$ ancillary ``shuttle'' qubits, and poses Dicke-state preparation as a \emph{closed-loop design} problem: given the target $(n,m)$, automatically infer collision strengths that maximize fidelity under practical constraints. Concretely, we formulate a two-parameter, bound-constrained optimization over intra-register and shuttle--register collision angles and solve it using a multi-start strategy with L-BFGS-B, yielding a reproducible controller prescription (optimized $γ_{\mathrm{in}}$, $γ_{\mathrm{sh}}$, and minimal-round convergence points) for each target. This removes the need for projective measurements and extends collisional entanglement generation beyond the single-excitation (W-state) sector to arbitrary $m$. Crucially, we optimize \emph{within} imperfect collisional dynamics where errors act throughout the sequence, including stochastic interaction dropouts (missing collisions) and standard decoherence channels. Strikingly, across wide error ranges the optimized controller preserves high preparation fidelity; imperfections manifest primarily as a modest increase in the required number of collision rounds. This behavior reflects a tunable competition in which noise suppresses correlations while properly chosen collisions continuously replenish them, allowing the control algorithm to trade time for fidelity.