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

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.

9 pages, 10 figures, 3 tables

References in corpus (6)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Quantum Natural Gradient
• Continuous-variable quantum neural networks
• Variational Quantum Linear Solver

Cited by in corpus (5)

• Barren Plateaus in Variational Quantum Computing
• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• Image Classification with Rotation-Invariant Variational Quantum Circuits
• Analyzing the quantum approximate optimization algorithm: ansätze, symmetries, and Lie algebras
• Expressivity of deterministic quantum computation with one qubit