# Neural network wave functions and the sign problem

arXiv: https://arxiv.org/abs/2002.04613 · HTML: https://mlsanity.com/paper/2002.04613/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2020.

## Built on by (most cited first, 20 of 20)

- [Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atze](https://mlsanity.com/paper/2112.07611/) (2021)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (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)
- [Deep learning of quantum entanglement from incomplete measurements](https://mlsanity.com/paper/2205.01462/) (2022)
- [Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems](https://mlsanity.com/paper/2206.07370/) (2022)
- [When can classical neural networks represent quantum states?](https://mlsanity.com/paper/2410.23152/) (2024)
- [Approximately-symmetric neural networks for quantum spin liquids](https://mlsanity.com/paper/2405.17541/) (2024)
- [Scaling of neural-network quantum states for time evolution](https://mlsanity.com/paper/2104.10696/) (2021)
- [Learning ground states of gapped quantum Hamiltonians with Kernel Methods](https://mlsanity.com/paper/2303.08902/) (2023)
- [Variational optimization of the amplitude of neural-network quantum many-body ground states](https://mlsanity.com/paper/2308.09664/) (2023)
- [Generalized Lanczos method for systematic optimization of neural-network quantum states](https://mlsanity.com/paper/2502.01264/) (2025)
- [O(N2) Universal Antisymmetry in Fermionic Neural Networks](https://mlsanity.com/paper/2205.13205/) (2022)
- [Probabilistic Computers for Neural Quantum States](https://mlsanity.com/paper/2512.24558/) (2025)
- [Low-variance estimators overcome the phase-gradient bottleneck in complex-valued neural quantum states](https://mlsanity.com/paper/2606.13912/) (2026)
- [Neural-network quantum state study of the long-range antiferromagnetic Ising chain](https://mlsanity.com/paper/2308.09709/) (2023)
- [Frankenstein Optimizer: Harnessing the Potential by Revisiting Optimization Tricks](https://mlsanity.com/paper/2503.02147/) (2025)
- [Enhanced Neural Quantum State via Annealed Gradient Descent](https://mlsanity.com/paper/2607.18865/) (2026)
- [Gradient-estimator design overcomes trainability barriers in neural-network-based variational optimization](https://mlsanity.com/paper/2609.22342/) (2026)
- [Apparent Compression, Real Stability: The Intrinsic Dimension of Learning a Quantum Wavefunction](https://mlsanity.com/paper/2609.33193/) (2026)

## Abstract (arXiv)

Neural quantum states (NQS) are a promising approach to study many-body quantum physics. However, they face a major challenge when applied to lattice models: Convolutional networks struggle to converge to ground states with a nontrivial sign structure. We tackle this problem by proposing a neural network architecture with a simple, explicit, and interpretable phase ansatz, which can robustly represent such states and achieve state-of-the-art variational energies for both conventional and frustrated antiferromagnets. In the latter case, our approach uncovers low-energy states that exhibit the Marshall sign rule and are therefore inconsistent with the expected ground state. Such states are the likely cause of the obstruction for NQS-based variational Monte Carlo to access the true ground states of these systems. We discuss the implications of this observation and suggest potential strategies to overcome the problem.