DysonNet: Constant-Time Local Updates for Neural Quantum States

TL;DR

DysonNet introduces a novel neural quantum state architecture that enables constant-time local updates, significantly improving training efficiency while maintaining accuracy, and offers a physically interpretable framework for scalable many-body wavefunction modeling.

Contribution

We propose DysonNet, a new NQS architecture that achieves constant-time local updates and scalable training complexity, bridging interpretability and efficiency in quantum many-body simulations.

Findings

Single-spin-flip updates computed in O(1) time, independent of system size.

Up to 230x speedup over Vision-Transformers in local estimator computation.

Achieves O(N log^2 N) training complexity, enabling scalable quantum state modeling.

Abstract

Neural quantum states (NQS) provide a flexible variational framework for many-body wavefunctions, but suffer from high computational cost and limited interpretability. We introduce DysonNet, a broad class of NQS that couples strictly local nonlinearities through global linear layers. This structure is analogous to a truncated Dyson series which gives an intuitive interpretation of local wavefunction updates as scattering from static impurities. By resumming the scattering series, single-spin-flip updates can be computed in $\mathcal{O}(1)$ time, independent of system size, using an algorithm we call ABACUS. Implementing DysonNet with the state-space model S4, we obtain up to $230\times$ speedups over Vision-Transformers for computing the local estimator. This corresponds to an asymptotic $\mathcal{O}(N^2)$ improvement in training-time scaling, reaching $\mathcal{O}(N \log^2 N)$ total training complexity in area-law phases. Benchmarks on the 1D long-range Ising model and frustrated $J_1$-$J_2$ chains show that DysonNet matches state-of-the-art NQS accuracy while removing the dominant local-update overhead. More broadly, our results suggest a route to scalable NQS architectures where physical interpretability directly enables computational efficiency.