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

TL;DR

This paper introduces physics-inspired transformer quantum states (PITQS) that leverage a latent imaginary-time evolution framework, resulting in more physically transparent, accurate, and parameter-efficient neural quantum state representations for complex quantum models.

Contribution

It proposes a novel physics-inspired transformer architecture for neural quantum states that enforces a static effective Hamiltonian and improves accuracy without increasing parameters.

Findings

PITQS achieve comparable or better accuracy than state-of-the-art TQS.

PITQS use fewer variational parameters than traditional methods.

Reinterpreting deep networks as latent cooling processes enhances physical interpretability.

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.