# Natural Evolutionary Strategies for Variational Quantum Computation

arXiv: https://arxiv.org/abs/2012.00101 · HTML: https://mlsanity.com/paper/2012.00101/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 15 of 15)

- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [Automatic design of quantum feature maps](https://mlsanity.com/paper/2105.12626/) (2021)
- [Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation](https://mlsanity.com/paper/2211.08737/) (2022)
- [Learning Interpretable Representations of Entanglement in Quantum Optics Experiments using Deep Generative Models](https://mlsanity.com/paper/2109.02490/) (2021)
- [Monte Carlo Tree Search based Hybrid Optimization of Variational Quantum Circuits](https://mlsanity.com/paper/2203.16707/) (2022)
- [The quantum cost function concentration dependency on the parametrization expressivity](https://mlsanity.com/paper/2301.06883/) (2023)
- [Evolution strategies: Application in hybrid quantum-classical neural networks](https://mlsanity.com/paper/2205.08059/) (2022)
- [AutoQML: Automatic Generation and Training of Robust Quantum-Inspired Classifiers by Using Genetic Algorithms on Grayscale Images](https://mlsanity.com/paper/2208.13246/) (2022)
- [Barren plateaus are amplified by the dimension of qudits](https://mlsanity.com/paper/2405.08190/) (2024)
- [Reinforcement learning to learn quantum states for Heisenberg scaling accuracy](https://mlsanity.com/paper/2412.02334/) (2024)
- [Randomized Benchmarking of Local Zeroth-Order Optimizers for Variational Quantum Systems](https://mlsanity.com/paper/2310.09468/) (2023)
- [Provably Robust Training of Quantum Circuit Classifiers Against Parameter Noise](https://mlsanity.com/paper/2505.18478/) (2025)
- [SparseMap: A Sparse Tensor Accelerator Framework Based on Evolution Strategy](https://mlsanity.com/paper/2508.12906/) (2025)
- [Information-Geometric Optimization on Spheres](https://mlsanity.com/paper/2606.07588/) (2026)

## Abstract (arXiv)

Natural evolutionary strategies (NES) are a family of gradient-free black-box optimization algorithms. This study illustrates their use for the optimization of randomly-initialized parametrized quantum circuits (PQCs) in the region of vanishing gradients. We show that using the NES gradient estimator the exponential decrease in variance can be alleviated. We implement two specific approaches, the exponential and separable natural evolutionary strategies, for parameter optimization of PQCs and compare them against standard gradient descent. We apply them to two different problems of ground state energy estimation using variational quantum eigensolver (VQE) and state preparation with circuits of varying depth and length. We also introduce batch optimization for circuits with larger depth to extend the use of evolutionary strategies to a larger number of parameters. We achieve accuracy comparable to state-of-the-art optimization techniques in all the above cases with a lower number of circuit evaluations. Our empirical results indicate that one can use NES as a hybrid tool in tandem with other gradient-based methods for optimization of deep quantum circuits in regions with vanishing gradients.