Intelligent Control of Collisional Architectures for Deterministic Multipartite State Engineering

TL;DR

The paper addresses the challenge of deterministically preparing multipartite Dicke states in collision-based architectures under realistic noise. It treats intra-register and shuttle–register collision strengths as design parameters and optimizes them using bound-constrained L-BFGS-B with multi-start initialization, within dynamics that include missing collisions and decoherence. The approach extends beyond single-excitation W states by enabling arbitrary m excitations and eliminates the need for shuttle measurements, achieving high fidelities up to n=14 in ideal conditions and demonstrating robustness across several noise models, at the cost of additional collision rounds. The work offers a physically transparent, scalable route to deterministic symmetric entanglement, with potential implementations in superconducting qubits and digital quantum simulators, and provides practical guidance on grid resolution and computational costs for optimization.

Abstract

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.

Figures (5)

• Figure 1: Collision scheme for preparing $|D_n^{(m)}\rangle$, i.e., an $n$-qubit Dicke state with $m$ excitations. In the case of $n=6$ and $m=2$, the procedure of the shuttle qubit $A_1$ consisting of discretized interaction steps (i, ii, iii, iv, i', ii, iii', iv') is repeated by the $A_2$ qubit.
• Figure 2: Minimal loss as a function of shuttle-register qubit interaction strength ($\gamma_{\mathrm{sh}}$) and intra-register qubit interaction strength ($\gamma_{\mathrm{in}}$). Red star denotes the optimal values yielding the minimum loss function based on the fidelity between the generated and ideal Dicke state, estimated by the L-BFGS-B simulation.
• Figure 3: Fidelity between the generated and the ideal Dicke states for sizes up to 14 qubits, across the accessible excitation sectors. Here, the simulation setup is based on a uniform grid with spacing $0.2$ radians over $\gamma_{\mathrm{in}}\in[0,\pi]$ and $\gamma_{\mathrm{sh}}\in[0.01,\pi]$.
• Figure 4: Robustness of the optimized collision protocol under experimentally motivated imperfections acting during the repeated-interaction dynamics for preparing $|D_5^{(2)}\rangle$ as an example. (a) Missing shuttle–register collisions: each scheduled shuttle–register interaction is skipped with a prescribed probability. (b) Decoherence channels (depolarizing, dephasing, amplitude damping): each independent noise channel acts throughout the collision process. For each imperfection strength, we rerun the bound-constrained optimization over $(\gamma_{\mathrm{in}},\gamma_{\mathrm{sh}})$ and report the maximum achieved fidelity with the target Dicke state (markers), alongside the corresponding noiseless baselines (dashed) and the ideal value $F=1$ (dotted).
• Figure 5: Fidelity between the generated and the ideal Dicke states for sizes up to 14 qubits, across various excitation sectors. Here, the simulation setup is based on a uniform grid with spacing $0.05$ radians over $\gamma_{\mathrm{in}}\in[0,\pi]$ and $\gamma_{\mathrm{sh}}\in[0.01,\pi]$.