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

TL;DR

This paper introduces a coordinate transformation strategy to enhance gradient-based optimization in machine learning, especially in quantum contexts, by mitigating local minima and barren plateaus, leading to faster and more efficient training.

Contribution

The paper proposes a novel coordinate transformation method that improves gradient methods in quantum machine learning, reducing computational costs and overcoming optimization challenges.

Findings

Significant performance improvements in quantum machine learning algorithms

Effective mitigation of barren plateaus and local minima

Enhanced exploration of the parameter landscape

Abstract

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.