# An Empirical Review of Optimization Techniques for Quantum Variational Circuits

arXiv: https://arxiv.org/abs/2202.01389 · HTML: https://mlsanity.com/paper/2202.01389/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 65 references that are in the map.
- First posted on arXiv 3 Feb 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [Reinforcement Learning with Quantum Variational Circuits](https://mlsanity.com/paper/2008.07524/) (2020)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atze](https://mlsanity.com/paper/2112.07611/) (2021)
- [On the Convergence Proof of AMSGrad and a New Version](https://mlsanity.com/paper/1904.03590/) (2019)
- [Policy Gradient based Quantum Approximate Optimization Algorithm](https://mlsanity.com/paper/2002.01068/) (2020)
- [Optimizing Quantum Variational Circuits with Deep Reinforcement Learning](https://mlsanity.com/paper/2109.03188/) (2021)
- [QuantumCircuitOpt: An Open-source Framework for Provably Optimal Quantum Circuit Design](https://mlsanity.com/paper/2111.11674/) (2021)

## Built on by (most cited first, 3 of 3)

- [Reinforcement learning with learned gadgets to tackle hard quantum problems on real hardware](https://mlsanity.com/paper/2411.00230/) (2024)
- [When cheap gradients fail: the measurement cost of attacking quantum classifiers](https://mlsanity.com/paper/2607.11095/) (2026)
- [QUBO-based training for VQAs on Quantum Annealers](https://mlsanity.com/paper/2509.01821/) (2025)

## Abstract (arXiv)

Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new parameters at every optimization step. However, this process can be extremely challenging, due to the nature of navigating the exponentially scaling complex Hilbert space, barren plateaus, and the noise present in all foreseeable quantum hardware. Although a variety of optimization algorithms are employed in practice, there is often a lack of theoretical or empirical motivations for this choice. To this end we empirically evaluate the potential of many common gradient and gradient free optimizers on a variety of optimization tasks. These tasks include both classical and quantum data based optimization routines. Our evaluations were conducted in both noise free and noisy simulations. The large number of problems and optimizers evaluated yields strong empirical guidance for choosing optimizers for QVCs that is currently lacking.