# Evolution strategies: Application in hybrid quantum-classical neural networks

arXiv: https://arxiv.org/abs/2205.08059 · HTML: https://mlsanity.com/paper/2205.08059/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 50 references that are in the map.
- First posted on arXiv 17 May 2022.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (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)
- [Advances in Quantum Deep Learning: An Overview](https://mlsanity.com/paper/2005.04316/) (2020)
- [Optimizing quantum heuristics with meta-learning](https://mlsanity.com/paper/1908.03185/) (2019)
- [Hybrid quantum convolutional neural networks model for COVID-19 prediction using chest X-Ray images](https://mlsanity.com/paper/2102.06535/) (2021)
- [Natural Evolutionary Strategies for Variational Quantum Computation](https://mlsanity.com/paper/2012.00101/) (2020)
- [Policy Gradient based Quantum Approximate Optimization Algorithm](https://mlsanity.com/paper/2002.01068/) (2020)
- [A hybrid quantum-classical neural network with deep residual learning](https://mlsanity.com/paper/2012.07772/) (2020)

## Built on by (most cited first, 5 of 5)

- [The quantum cost function concentration dependency on the parametrization expressivity](https://mlsanity.com/paper/2301.06883/) (2023)
- [Restricting to the chip architecture maintains the quantum neural network accuracy](https://mlsanity.com/paper/2212.14426/) (2022)
- [Barren plateaus are amplified by the dimension of qudits](https://mlsanity.com/paper/2405.08190/) (2024)
- [Quantum-AI empowered Intelligent Surveillance: Advancing Public Safety Through Innovative Contraband Detection](https://mlsanity.com/paper/2309.03231/) (2023)
- [Quantum-Evolutionary Neural Networks for Multi-Agent Federated Learning](https://mlsanity.com/paper/2505.15836/) (2025)

## Abstract (arXiv)

With the rapid development of quantum computers, several applications are being proposed for them. Quantum simulations, simulation of chemical reactions, solution of optimization problems and quantum neural networks (QNNs) are some examples. However, problems such as noise, limited number of qubits and circuit depth, and gradient vanishing must be resolved before we can use them to their full potential. In the field of quantum machine learning, several models have been proposed. In general, in order to train these different models, we use the gradient of a cost function with respect to the model parameters. In order to obtain this gradient, we must compute the derivative of this function with respect to the model parameters. One of the most used methods in the literature to perform this task is the parameter-shift rule method. This method consists of evaluating the cost function twice for each parameter of the QNN. A problem with this method is that the number of evaluations grows linearly with the number of parameters. In this work we study an alternative method, called Evolution Strategies (ES), which are a family of black box optimization algorithms which iteratively update the parameters using a search gradient. An advantage of the ES method is that in using it one can control the number of times the cost function will be evaluated. We apply the ES method to the binary classification task, showing that this method is a viable alternative for training QNNs. However, we observe that its performance will be strongly dependent on the hyperparameters used. Furthermore, we also observe that this method, alike the parameter shift rule method, suffers from the problem of gradient vanishing.