# Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo

arXiv: https://arxiv.org/abs/2605.13807 · HTML: https://mlsanity.com/paper/2605.13807/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 61 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Parallelizing Linear Recurrent Neural Nets Over Sequence Length](https://mlsanity.com/paper/1709.04057/) (2017)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Effectively Modeling Time Series with Simple Discrete State Spaces](https://mlsanity.com/paper/2303.09489/) (2023)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models](https://mlsanity.com/paper/2101.07243/) (2021)
- [From Tensor Network Quantum States to Tensorial Recurrent Neural Networks](https://mlsanity.com/paper/2206.12363/) (2022)
- [Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice](https://mlsanity.com/paper/2405.20384/) (2024)
- [Solving the Hubbard model with Neural Quantum States](https://mlsanity.com/paper/2507.02644/) (2025)
- [Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systems](https://mlsanity.com/paper/2407.18057/) (2024)
- [Graph-Theoretic Analysis of Phase Optimization Complexity in Variational Wave Functions for Heisenberg Antiferromagnets](https://mlsanity.com/paper/2602.04943/) (2026)
- [Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum States](https://mlsanity.com/paper/2604.08661/) (2026)

## Built on by (most cited first, 2 of 2)

- [Representability-Aware Neural Networks for Reduced Density Matrices: Application to Fractional Chern Insulators](https://mlsanity.com/paper/2605.20326/) (2026)
- [One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective](https://mlsanity.com/paper/2607.02292/) (2026)

## Abstract (arXiv)

Neural-network quantum states have emerged as a powerful variational framework for quantum many-body systems, with recent progress often driven by massively parallel architectures such as transformers. Recurrent neural network quantum states, however, are frequently regarded as intrinsically sequential and therefore less scalable. Here we revisit this view by showing that modern recurrent architectures can support fast, accurate, and computationally accessible neural quantum state simulations. Using autoregressive recurrent wave functions together with recent advances in parallelizable recurrence, we develop variational ans"atze, called parallel scan recurrent neural quantum states (PSR-NQS), which can be trained efficiently within variational Monte Carlo in one and two spatial dimensions. We demonstrate accurate benchmark results and show that, with iterative retraining, our approach reaches two-dimensional spin lattices as large as 52×52 while remaining in agreement with available quantum Monte Carlo data. Our results establish recurrent architectures as a practical and promising route toward scalable neural quantum state simulations with modest computational resources.