用神经量子态解决量子嵌入问题，精度接近精确解。
Neural-Quantum-States Impurity Solver for Quantum Embedding Problems
- 基于图Transformer的神经量子态，可处理任意连接的杂质轨道。
- 在安德森晶格模型上，结果与精确对角化法高度一致。
- 计算瓶颈在于可观测量采样，而非变分优化，需更高效推理方法。
神经量子态（NQS）因其可扩展性和灵活性，成为求解二次量化哈密顿量的有前景方法。本文设计并评估了一种用于量子嵌入（QE）方法的NQS杂质求解器，聚焦于鬼谷-盖茨威勒近似（gGA）框架。我们提出一种基于图Transformer的NQS框架，能够表示嵌入哈密顿量中任意连接的杂质轨道，并开发了误差控制机制以稳定QE循环中的迭代更新。通过安德森晶格模型的基准gGA计算验证了方法的准确性，结果与精确对角化求解器高度一致。最后，我们的计算开销分析表明，该方法的主要瓶颈是嵌入循环中高精度可观测量采样，而非NQS变分优化，直接凸显了更高效推理技术的关键需求。
原文摘要 · Abstract (English)
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.
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