Regularization of Riemannian optimization: Application to process tomography and quantum machine learning

TL;DR

This paper explores how adding regularization terms to Riemannian gradient descent algorithms improves quantum process tomography and quantum machine learning by enhancing convergence, fidelity, and interpretability.

Contribution

It introduces rank-penalizing regularization to Riemannian optimization, demonstrating improved performance and interpretability in quantum applications.

Findings

Faster convergence in quantum process tomography

Higher fidelities achieved with regularization

Simplified quantum classifiers without loss of accuracy

Abstract

Gradient descent algorithms on Riemannian manifolds have been used recently for the optimization of quantum channels. In this contribution, we investigate the influence of various regularization terms added to the cost function of these gradient descent approaches. Motivated by Lasso regularization, we apply penalties for large ranks of the quantum channel, favoring solutions that can be represented by as few Kraus operators as possible. We apply the method to quantum process tomography and a quantum machine learning problem. Suitably regularized models show faster convergence of the optimization as well as better fidelities in the case of process tomography. Applied to quantum classification scenarios, the regularization terms can simplify the classifying quantum channel without degrading the accuracy of the classification, thereby revealing the minimum channel rank needed for the given input data.