# Hybrid Ground-State Quantum Algorithms based on Neural Schr"odinger Forging

arXiv: https://arxiv.org/abs/2307.02633 · HTML: https://mlsanity.com/paper/2307.02633/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 61 references that are in the map.
- First posted on arXiv 5 Jul 2023.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [Autoregressive neural-network wavefunctions for ab initio quantum chemistry](https://mlsanity.com/paper/2109.12606/) (2021)
- [Variational Quantum Eigensolver for Frustrated Quantum Systems](https://mlsanity.com/paper/2005.00544/) (2020)
- [Learning ground states of gapped quantum Hamiltonians with Kernel Methods](https://mlsanity.com/paper/2303.08902/) (2023)

## Abstract (arXiv)

Entanglement forging based variational algorithms leverage the bi-partition of quantum systems for addressing ground state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis states, or bitstrings, when performing the Schmidt decomposition of the whole system. To overcome this challenge, we propose a new method for entanglement forging employing generative neural networks to identify the most pertinent bitstrings, eliminating the need for the exponential sum. Through empirical demonstrations on systems of increasing complexity, we show that the proposed algorithm achieves comparable or superior performance compared to the existing standard implementation of entanglement forging. Moreover, by controlling the amount of required resources, this scheme can be applied to larger, as well as non permutation invariant systems, where the latter constraint is associated with the Heisenberg forging procedure. We substantiate our findings through numerical simulations conducted on spins models exhibiting one-dimensional ring, two-dimensional triangular lattice topologies, and nuclear shell model configurations.