# Variational Optimization for Quantum Problems using Deep Generative Networks

arXiv: https://arxiv.org/abs/2404.18041 · HTML: https://mlsanity.com/paper/2404.18041/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 87 references that are in the map.
- First posted on arXiv 28 Apr 2024.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Drug discovery with explainable artificial intelligence](https://mlsanity.com/paper/2007.00523/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Which Neural Net Architectures Give Rise To Exploding and Vanishing Gradients?](https://mlsanity.com/paper/1801.03744/) (2018)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows](https://mlsanity.com/paper/2007.02731/) (2020)
- [On scientific understanding with artificial intelligence](https://mlsanity.com/paper/2204.01467/) (2022)
- [Monge-Amp`ere Flow for Generative Modeling](https://mlsanity.com/paper/1809.10188/) (2018)
- [Capacity and quantum geometry of parametrized quantum circuits](https://mlsanity.com/paper/2102.01659/) (2021)
- [Learning hard quantum distributions with variational autoencoders](https://mlsanity.com/paper/1710.00725/) (2017)
- [Learning Unitary Operators with Help From u(n)](https://mlsanity.com/paper/1607.04903/) (2016)
- [Quantum device fine-tuning using unsupervised embedding learning](https://mlsanity.com/paper/2001.04409/) (2020)
- [Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems](https://mlsanity.com/paper/2010.00157/) (2020)

## Abstract (arXiv)

Optimization drives advances in quantum science and machine learning, yet most generative models aim to mimic data rather than to discover optimal answers to challenging problems. Here we present a variational generative optimization network that learns to map simple random inputs into high quality solutions across a variety of quantum tasks. We demonstrate that the network rapidly identifies entangled states exhibiting an optimal advantage in entanglement detection when allowing classical communication, attains the ground state energy of an eighteen spin model without encountering the barren plateau phenomenon that hampers standard hybrid algorithms, and-after a single training run-outputs multiple orthogonal ground states of degenerate quantum models. Because the method is model agnostic, parallelizable and runs on current classical hardware, it can accelerate future variational optimization problems in quantum information, quantum computing and beyond.