# Improving Gradient Methods via Coordinate Transformations: Applications to Quantum Machine Learning

arXiv: https://arxiv.org/abs/2304.06768 · HTML: https://mlsanity.com/paper/2304.06768/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 13 Apr 2023.

## Builds on (most cited first, 1 of 1)

- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)

## Built on by (most cited first, 7 of 7)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [Quantum-PEFT: Ultra parameter-efficient fine-tuning](https://mlsanity.com/paper/2503.05431/) (2025)
- [Quantum Large Language Models via Tensor Network Disentanglers](https://mlsanity.com/paper/2410.17397/) (2024)
- [Image Classification with Rotation-Invariant Variational Quantum Circuits](https://mlsanity.com/paper/2403.15031/) (2024)
- [Expressivity of deterministic quantum computation with one qubit](https://mlsanity.com/paper/2411.02751/) (2024)
- [Inductive Graph Representation Learning with Quantum Graph Neural Networks](https://mlsanity.com/paper/2503.24111/) (2025)

## Abstract (arXiv)

Machine learning algorithms, both in their classical and quantum versions, heavily rely on optimization algorithms based on gradients, such as gradient descent and alike. The overall performance is dependent on the appearance of local minima and barren plateaus, which slow-down calculations and lead to non-optimal solutions. In practice, this results in dramatic computational and energy costs for AI applications. In this paper we introduce a generic strategy to accelerate and improve the overall performance of such methods, allowing to alleviate the effect of barren plateaus and local minima. Our method is based on coordinate transformations, somehow similar to variational rotations, adding extra directions in parameter space that depend on the cost function itself, and which allow to explore the configuration landscape more efficiently. The validity of our method is benchmarked by boosting a number of quantum machine learning algorithms, getting a very significant improvement in their performance.