# Deep autoregressive models for the efficient variational simulation of many-body quantum systems

arXiv: https://arxiv.org/abs/1902.04057 · HTML: https://mlsanity.com/paper/1902.04057/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2019.

## Built on by (most cited first, 30 of 64)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [The Inductive Bias of In-Context Learning: Rethinking Pretraining Example Design](https://mlsanity.com/paper/2110.04541/) (2021)
- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics](https://mlsanity.com/paper/2502.08696/) (2025)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [Neural tensor contractions and the expressive power of deep neural quantum states](https://mlsanity.com/paper/2103.10293/) (2021)
- [Tensor networks for unsupervised machine learning](https://mlsanity.com/paper/2106.12974/) (2021)
- [Autoregressive neural-network wavefunctions for ab initio quantum chemistry](https://mlsanity.com/paper/2109.12606/) (2021)
- [Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models](https://mlsanity.com/paper/2101.07243/) (2021)
- [Which transformer architecture fits my data? A vocabulary bottleneck in self-attention](https://mlsanity.com/paper/2105.03928/) (2021)
- [Neural Error Mitigation of Near-Term Quantum Simulations](https://mlsanity.com/paper/2105.08086/) (2021)
- [Learning ground states of quantum Hamiltonians with graph networks](https://mlsanity.com/paper/2110.06390/) (2021)
- [Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctions](https://mlsanity.com/paper/2212.06835/) (2022)
- [Pairing-based graph neural network for simulating quantum materials](https://mlsanity.com/paper/2311.02143/) (2023)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Spacetime Neural Network for High Dimensional Quantum Dynamics](https://mlsanity.com/paper/2108.02200/) (2021)
- [Scalable neural quantum states architecture for quantum chemistry](https://mlsanity.com/paper/2208.05637/) (2022)
- [Neural-network solutions to stochastic reaction networks](https://mlsanity.com/paper/2210.01169/) (2022)
- [The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systems](https://mlsanity.com/paper/2302.08347/) (2023)
- [ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation](https://mlsanity.com/paper/2304.01996/) (2023)
- [NNQS-Transformer: an Efficient and Scalable Neural Network Quantum States Approach for Ab initio Quantum Chemistry](https://mlsanity.com/paper/2306.16705/) (2023)
- [Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems](https://mlsanity.com/paper/2206.07370/) (2022)
- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (2023)
- [Certifying almost all quantum states with few single-qubit measurements](https://mlsanity.com/paper/2404.07281/) (2024)
- [Transferable Neural Wavefunctions for Solids](https://mlsanity.com/paper/2405.07599/) (2024)
- [Rayleigh-Gauss-Newton optimization with enhanced sampling for variational Monte Carlo](https://mlsanity.com/paper/2106.10558/) (2021)
- [Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy](https://mlsanity.com/paper/2207.14314/) (2022)

## Abstract (arXiv)

Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most notably the use of Markov-Chain Monte-Carlo (MCMC) sampling to estimate quantum expectations. The local stochastic sampling in MCMC caps the potential advantages of neural networks in two ways: (i) Its intrinsic computational cost sets stringent practical limits on the width and depth of the networks, and therefore limits their expressive capacity; (ii) Its difficulty in generating precise and uncorrelated samples can result in estimations of observables that are very far from their true value. Inspired by the state-of-the-art generative models used in machine learning, we propose a specialized Neural Network architecture that supports efficient and exact sampling, completely circumventing the need for Markov Chain sampling. We demonstrate our approach for two-dimensional interacting spin models, showcasing the ability to obtain accurate results on larger system sizes than those currently accessible to neural-network quantum states.