Neural quantum states (NQS) have emerged as a promising approach to solve second-quantized Hamiltonians, because of their scalability and flexibility. In this work, we design and benchmark an NQS impurity solver for the quantum embedding (QE) methods, focusing on the ghost Gutzwiller Approximation (gGA) framework. We introduce a graph transformer-based NQS framework able to represent arbitrarily connected impurity orbitals of the embedding Hamiltonian (EH) and develop an error control mechanism to stabilize iterative updates throughout the QE loops. We validate the accuracy of our approach with benchmark gGA calculations of the Anderson Lattice Model, yielding results in excellent agreement with the exact diagonalisation impurity solver. Finally, our analysis of the computational budget reveals the method's principal bottleneck to be the high-accuracy sampling of physical observables required by the embedding loop, rather than the NQS variational optimization, directly highlighting the critical need for more efficient inference techniques.

翻译：神经量子态（NQS）因其可扩展性和灵活性，已成为求解二次量子化哈密顿量的一种有前景的方法。在本工作中，我们设计并基准测试了一种用于量子嵌入（QE）方法的NQS杂质求解器，重点关注幽灵古兹维勒近似（gGA）框架。我们引入了一种基于图变换器的NQS框架，能够表示嵌入哈密顿量（EH）中任意连接的杂质轨道，并开发了一种误差控制机制以稳定整个QE循环中的迭代更新。我们通过安德森晶格模型的基准gGA计算验证了该方法的准确性，所得结果与精确对角化杂质求解器高度吻合。最后，我们对计算开销的分析表明，该方法的主要瓶颈在于嵌入循环所需物理观测量的高精度采样，而非NQS变分优化，这直接凸显了对更高效推理技术的迫切需求。