Regularizing quantum loss landscapes by noise injection

TL;DR

This paper introduces a noise injection protocol that smooths quantum loss landscapes by suppressing high-frequency components, improving the training efficiency of variational quantum algorithms.

Contribution

The authors propose a novel noise injection method that regularizes quantum loss landscapes, enhancing optimization and solution quality in quantum machine learning models.

Findings

Significant improvement in solution quality across various problems.

Robustness of the method in both hardware and simulations.

Compatibility with existing optimization techniques like quantum natural gradient.

Abstract

The difficulty of training variational quantum algorithms and quantum machine learning models is well established. In particular, quantum loss landscapes are often highly non-convex and dominated by poor local minima. While this renders their training NP-hard in general, efficient heuristics that work well for typical instances may still exist. Here, we propose a protocol that uses a targeted noise injection to smooth and regularize quantum loss landscapes. It works by exponentially suppressing the high-frequency components in the Fourier expansion of the quantum loss function. The protocol can be efficiently implemented both in hardware and in simulations. We observe significant and robust improvements of solution quality across various problem types. Our method can be combined with existing techniques mitigating the local minima, such as the quantum natural gradient optimizer, and adds to the toolbox of methods for optimizing quantum loss functions.