We propose a graph method for systematically searching for schemes that can generate multipartite entanglement in linear bosonic systems with heralding. While heralded entanglement generation offers more tolerable schemes for quantum tasks than postselected ones, it is generally more challenging to find appropriate circuits for multipartite systems. We show that our graph mapping from boson subtractions provides handy tactics to overcome the limitations in circuit designs. Within our graph framework, we identify enhanced schemes for qubit N-partite GHZ, W, and the superposition of N = 3 GHZ and W states. Furthermore, we have found a qudit N-partite GHZ state generation scheme, which requires substantially fewer particles than previous proposals. These results demonstrate the power of our approach in discovering optimized solutions for the generation of intricate heralded entangled states. We expect our method to serve as a promising tool in generating diverse entanglement.

我们提出了一种图方法，用于系统地搜索可以在带有预示的线性玻色子系统中生成多部分纠缠的方案。虽然预示着的纠缠生成为量子任务提供了比后选择方案更可容忍的方案，但为多部分系统找到合适的电路通常更具挑战性。我们表明，我们的玻色子减法图映射提供了克服电路设计限制的便捷策略。在我们的图框架内，我们确定了量子位 N 部分 GHZ、W 以及 N = 3 GHZ 和 W 状态叠加的增强方案。此外，我们还发现了一种 qdit N 部分 GHZ 状态生成方案，该方案所需的粒子比以前的方案少得多。这些结果证明了我们的方法在发现生成复杂的预示纠缠态的优化解决方案方面的力量。我们希望我们的方法能够成为产生多样化纠缠的有前途的工具。