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 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 diagonalization 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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• Density of states
• Electronic structure of atoms & molecules
• Phase transitions
• Quasiparticles & collective excitations
• Strongly correlated systems
• Anderson impurity model
• Artificial neural networks
• Gutzwiller approximation
• Quantum Monte Carlo