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.

References

To the best of our knowledge, this is mostly due to the fact that it is not clear at first sight and which NQS architecture is most suitable for a given physical problem is a major open question in the field.

— From Architectures to Applications: A Review of Neural Quantum States  (2402.09402 - Lange et al., 2024) in Section 2 (NQS Architectures), paragraph following Figure 2 (timeline)

Also, with our current computing resources, while it is not feasible to carry out the computations for the $N=26$ case, it is natural to wonder whether, at $N=26$, HRBM would continue to outperform RBM, given the trends shown in Fig.\ref{main_scaling_res}, where RBM displays a non-monotonic optimization trajectory with an error spike at $N=20$ whereas HRBM displays a monotonic trajectory. Could this mean that at $N=26$, RBM would outperform HRBM in terms of relative energy error, energy variance and reconstruction errors?

— Hyperbolic Restricted Boltzmann Machine Neural Quantum State  (2609.26032 - Dao, 22 Sep 2026) in Section 3, Subsection “Full entanglement spectrum results” (Section 3.2)