Identify the most suitable NQS architecture for a given physical problem

Determine, for a given quantum many-body problem, which neural quantum state architecture (e.g., feed-forward neural networks, restricted Boltzmann machines, convolutional neural networks, graph neural networks, transformers, autoregressive recurrent networks, or fermionic variants) is most suitable for achieving accurate and efficient simulations, and establish principled criteria for selecting among these architectures based on problem characteristics.

Background

The review surveys a wide range of neural quantum state (NQS) architectures and documents their applications across spin, bosonic, fermionic, finite-temperature, dynamical, and open-system settings. Despite numerous successes, different architectures often perform comparably across benchmarks, and results depend sensitively on design choices and optimization strategies.

The authors note that recent literature employs many different architectures in roughly similar proportions, reflecting a lack of consensus on how to match architectures to specific physical problems. Establishing clear guidelines or criteria for architecture selection remains a central unresolved issue, with implications for performance, scalability, and reliability of NQS-based simulations.