Physics-inspired transformer quantum states via latent imaginary-time evolution

2026-02-03

AI Summary

This work addresses the limited physical interpretability and difficulty in systematic optimization of conventional Transformer-based neural quantum states. The authors propose a physics-inspired modeling framework that interprets neural quantum states as neural approximations of imaginary-time evolution in a latent space. By introducing a static effective Hamiltonian and employing a Trotter–Suzuki decomposition, they construct an interpretable architecture enhanced with inter-layer weight sharing and a high-precision propagation mechanism. This design improves both expressive power and physical consistency without increasing the number of variational parameters. Numerical experiments on the J₁–J₂ Heisenberg model demonstrate that the proposed method achieves or surpasses the accuracy of state-of-the-art Transformer quantum states while using significantly fewer variational parameters.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Neural quantum states (NQS) are powerful ans\"atze in the variational Monte Carlo framework, yet their architectures are often treated as black boxes. We propose a physically transparent framework in which NQS are treated as neural approximations to latent imaginary-time evolution. This viewpoint suggests that standard Transformer-based NQS (TQS) architectures correspond to physically unmotivated effective Hamiltonians dependent on imaginary time in a latent space. Building on this interpretation, we introduce physics-inspired transformer quantum states (PITQS), which enforce a static effective Hamiltonian by sharing weights across layers and improve propagation accuracy via Trotter-Suzuki decompositions without increasing the number of variational parameters. For the frustrated $J_1$-$J_2$ Heisenberg model, our ans\"atze achieve accuracies comparable to or exceeding state-of-the-art TQS while using substantially fewer variational parameters. This study demonstrates that reinterpreting the deep network structure as a latent cooling process enables a more physically grounded, systematic, and compact design, thereby bridging the gap between black-box expressivity and physically transparent construction.

Problem

• neural quantum states
• Transformer
• imaginary-time evolution
• effective Hamiltonian
• physical transparency

Innovation

• Physics-inspired Transformer
• Neural Quantum States
• Imaginary-time Evolution
• Trotter-Suzuki Decomposition
• Variational Monte Carlo