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.
", "doi": "10.1103/rkd8-q6yl", "issn": "2469-9950", "publisher": "American Physical Society", "publication": "Physical Review B", "publication_date": "2026-04-10", "series_number": "15", "volume": "113", "issue": "15", "pages": "155123" }, { "id": "authors:qagg3-m8v16", "collection": "authors", "collection_id": "qagg3-m8v16", "cite_using_url": "https://authors.library.caltech.edu/records/qagg3-m8v16", "type": "article", "title": "Neuralized fermionic tensor networks for quantum many-body systems", "author": [ { "family_name": "Du", "given_name": "Si-Jing", "orcid": "0000-0002-4737-9308", "clpid": "Du-Si-Jing" }, { "family_name": "Chen", "given_name": "Ao", "orcid": "0000-0002-5021-5160", "clpid": "Chen-Ao" }, { "family_name": "Chan", "given_name": "Garnet Kin-Lic", "orcid": "0000-0001-8009-6038", "clpid": "Chan-Garnet-K-L" } ], "abstract": "We describe a class of neuralized fermionic tensor network states (NN-fTNSs) that introduce nonlinearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction uses the fTNS algebra to implement a natural fermionic sign structure and is compatible with standard tensor network algorithms but gains enhanced expressivity through the neural network parametrization. Using the 1D and 2D Fermi-Hubbard models as benchmarks, we demonstrate that NN-fTNSs achieve order of magnitude improvements in the ground-state energy compared to pure fTNSs with the same bond dimension and can be systematically improved through both the tensor network bond dimension and the neural network parametrization. Compared to existing fermionic neural quantum states based on Slater determinants and Pfaffians, NN-fTNSs offer a physically motivated alternative fermionic structure. Furthermore, compared to such states, NN-fTNSs naturally exhibit improved computational scaling and we demonstrate a construction that achieves linear scaling with the lattice size.
", "doi": "10.1103/x8vl-qf14", "issn": "2469-9950", "publisher": "American Physical Society", "publication": "Physical Review B", "publication_date": "2026-02-19", "series_number": "8", "volume": "113", "issue": "8", "pages": "085134" } ]