Neural-Quantum-States Impurity Solver for Quantum Embedding Problems

2025-09-15

AI Summary

Conventional impurity solvers in quantum embedding methods exhibit limited modeling flexibility and numerical instability for strongly correlated systems—particularly within the generalized Gutzwiller approximation (gGA) framework. Method: We propose a novel impurity solver based on neural quantum states (NQS), integrating a graph transformer network to adaptively represent impurity orbitals of arbitrary topologies and incorporating an error-control mechanism to ensure convergence of nested variational Monte Carlo iterations. Crucially, we identify sampling fidelity—not optimization—as the primary computational bottleneck, underscoring the necessity of efficient inference. Contribution/Results: Benchmarking on the Anderson lattice model under gGA, our approach achieves quantitative agreement with exact diagonalization for key physical observables, demonstrating high accuracy and robustness. This work pioneers the integration of graph neural networks with NQS for quantum embedding impurity solving, establishing a scalable, high-fidelity general-purpose framework for strongly correlated many-body problems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Neural quantum states (NQS) have emerged as a promising approach to solve second-quantised Hamiltonians, because of their scalability and flexibility. In this work, we design and benchmark an NQS impurity solver for the quantum embedding methods, focusing on the ghost Gutzwiller Approximation (gGA) framework. We introduce a graph transformer-based NQS framework able to represent arbitrarily connected impurity orbitals and develop an error control mechanism to stabilise iterative updates throughout the quantum embedding 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 optimisation, directly highlighting the critical need for more efficient inference techniques.

Problem

• Develops a neural quantum state impurity solver
• Integrates solver into quantum embedding methods
• Addresses sampling bottlenecks in observable calculations

Innovation

• Graph transformer-based NQS framework
• Error control mechanism for iterative updates
• High-accuracy sampling of observables