Noise-Induced Equalization in quantum learning models

TL;DR

This paper investigates how a specific level of quantum noise can improve the optimization landscape and generalization in quantum machine learning models by inducing an equalization effect, supported by theoretical analysis and numerical simulations.

Contribution

It introduces a pre-training procedure to identify optimal quantum noise levels that enhance learning by equalizing sensitivity across principal directions in the parameter space.

Findings

Optimal noise levels induce landscape equalization.

Noise can improve generalization in quantum models.

Numerical simulations confirm beneficial effects near optimal noise levels.

Abstract

Quantum noise is known to strongly affect quantum computation, thus potentially limiting the performance of currently available quantum processing units. Even learning models based on variational quantum algorithms, which were designed to cope with the limitations of state-of-the art noisy hardware capabilities, are affected by noise-induced barren plateaus, arising when the noise level becomes too strong. However, the generalization performances of such quantum machine learning algorithms can also be positively influenced by a proper level of noise, despite its generally detrimental effects. Here, we propose a pre-training procedure to determine the quantum noise level leading to desirable optimisation landscape properties. We show that an optimized level of quantum noise induces an ``equalization'' of the directions in the Riemannian manifold, flattening(/enhancing) the initially steep(/shallow) ones by redistributing sensitivity across its principal eigen-directions. We analyse this noise-induced equalization through the lens of the Quantum Fisher Information Matrix, thus providing a recipe that allows to estimate the noise level inducing the strongest equalization. We finally benchmark these conclusions with extensive numerical simulations providing evidence of the beneficial noise effects in the neighborhood of the best equalization, often leading to improved generalization.