For the first time, we implement the deep-neural-network-based variational Monte Carlo approach for the multiquark bound states, whose complexity surpasses that of electron or nucleon systems due to strong SU(3) color interactions. We design a novel and high-efficiency architecture, DeepQuark, to address the unique challenges in multiquark systems such as stronger correlations, extra discrete quantum numbers, and intractable confinement interaction. Our method demonstrates competitive performance with state-of-the-art approaches, including diffusion Monte Carlo and Gaussian expansion method, in the nucleon, doubly heavy tetraquark, and fully heavy tetraquark systems. Notably, it outperforms existing calculations for pentaquarks, exemplified by the triply heavy pentaquark. For the nucleon, we successfully incorporate three-body flux-tube confinement interactions without additional computational costs. In tetraquark systems, we consistently describe hadronic molecule $T_{cc}$ and compact tetraquark $T_{bb}$ with an unbiased form of wave function ansatz. In the pentaquark sector, we obtain weakly bound $\bar D^*Ξ_{cc}^*$ molecule $P_{cc\bar c}(5715)$ with $S=\frac{5}{2}$ and its bottom partner $P_{bb\bar b}(15569)$. They can be viewed as the analogs of the molecular $T_{cc}$. We recommend experimental search of $P_{cc\bar c}(5715)$ in the D-wave $J/ψΛ_c$ channel. DeepQuark holds great promise for extension to larger multiquark systems, overcoming the computational barriers in conventional methods. It also serves as a powerful framework for exploring confining mechanism beyond two-body interactions in multiquark states, which may offer valuable insights into nonperturbative QCD and general many-body physics.

翻译：我们首次将基于深度神经网络的变分蒙特卡洛方法应用于多夸克束缚态体系。由于强SU(3)色相互作用的存在，该体系的复杂度超越了电子或核子系统。针对多夸克系统中更强的关联效应、额外的离散量子数以及难以处理的禁闭相互作用等独特挑战，我们设计了一种新颖高效的架构——DeepQuark。在核子、双重重四夸克及全重四夸克体系中，我们的方法展现出与扩散蒙特卡洛和高斯展开法等前沿技术相竞争的性能。尤其值得注意的是，该方法在三重重五夸克等五夸克体系的计算中超越了现有结果。对于核子体系，我们成功引入了三体流管禁闭相互作用，且未增加额外计算成本。在四夸克体系中，我们采用无偏形式的波函数拟设，一致性地描述了强子分子态$T_{cc}$与紧致四夸克态$T_{bb}$。在五夸克领域，我们获得了弱束缚的$\bar D^*Ξ_{cc}^*$分子态$P_{cc\bar c}(5715)$（自旋$S=\frac{5}{2}$）及其底夸克对应态$P_{bb\bar b}(15569)$，它们可视为分子态$T_{cc}$的类比物。我们建议在D波$J/ψΛ_c$道中开展对$P_{cc\bar c}(5715)$的实验搜寻。DeepQuark在扩展至更大规模多夸克体系方面具有巨大潜力，能够突破传统方法的计算壁垒。该框架还可作为探索多夸克态中超越二体相互作用的禁闭机制的有力工具，有望为非微扰QCD及广义多体物理研究提供重要见解。