# Quantum Optimization for Training Quantum Neural Networks

arXiv: https://arxiv.org/abs/2103.17047 · HTML: https://mlsanity.com/paper/2103.17047/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 77 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 13 of 13)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Learning to learn with quantum neural networks via classical neural networks](https://mlsanity.com/paper/1907.05415/) (2019)
- [Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems](https://mlsanity.com/paper/1911.11071/) (2019)
- [Learning and Inference on Generative Adversarial Quantum Circuits](https://mlsanity.com/paper/1808.03425/) (2018)
- [Policy Gradient based Quantum Approximate Optimization Algorithm](https://mlsanity.com/paper/2002.01068/) (2020)
- [Reinforcement-Learning-Based Variational Quantum Circuits Optimization for Combinatorial Problems](https://mlsanity.com/paper/1911.04574/) (2019)
- [Low depth mechanisms for quantum optimization](https://mlsanity.com/paper/2008.08615/) (2020)
- [A Quantum Walk Enhanced Grover Search Algorithm for Global Optimization](https://mlsanity.com/paper/1711.07825/) (2017)

## Built on by (most cited first, 6 of 6)

- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Variational Quantum Neural Networks (VQNNS) in Image Classification](https://mlsanity.com/paper/2303.05860/) (2023)
- [Graph Neural Networks on Quantum Computers](https://mlsanity.com/paper/2405.17060/) (2024)
- [Quantum Extremal Learning](https://mlsanity.com/paper/2205.02807/) (2022)
- [Automatic re-calibration of quantum devices by reinforcement learning](https://mlsanity.com/paper/2404.10726/) (2024)
- [Hybrid Classical-Quantum architecture for vectorised image classification of hand-written sketches](https://mlsanity.com/paper/2407.06416/) (2024)

## Abstract (arXiv)

Training quantum neural networks (QNNs) using gradient-based or gradient-free classical optimisation approaches is severely impacted by the presence of barren plateaus in the cost landscapes. In this paper, we devise a framework for leveraging quantum optimisation algorithms to find optimal parameters of QNNs for certain tasks. To achieve this, we coherently encode the cost function of QNNs onto relative phases of a superposition state in the Hilbert space of the network parameters. The parameters are tuned with an iterative quantum optimisation structure using adaptively selected Hamiltonians. The quantum mechanism of this framework exploits hidden structure in the QNN optimisation problem and hence is expected to provide beyond-Grover speed up, mitigating the barren plateau issue.