Improving Quantum Neural Networks exploration by Noise-Induced Equalization

TL;DR

This work tackles how quantum noise on NISQ devices affects quantum neural networks (QNNs), showing that while strong noise harms training, a moderate noise level can improve generalization via noise-induced equalization (NIE) of the Quantum Fisher Information Matrix (QFIM) eigenspectrum. It introduces a pre-training procedure to identify the optimal noise level $p^*$ by examining the spectrally-resolved changes in QFIM eigenvalues, and demonstrates that near $p^*$ the optimization landscape becomes smoother, enhancing exploration over exploitation. Numerical experiments across under- and overparameterized QNNs and multiple noise channels confirm NIE and show alignment between $p^*$ and noise levels that minimize test MSE, offering a practical regularization strategy without extensive hyperparameter search. The method is architecture- and dataset-agnostic, and the authors discuss connections to generalization bounds and potential extensions to meta-learning and broader quantum information tasks.

Abstract

Quantum noise is known to strongly affect quantum computation, thus potentially limiting the performance of currently available quantum processing units. Even models of quantum neural networks 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 optimization landscape properties. We show that an optimal quantum noise level induces an ``equalization'' of variational parameters: the least important parameters gain relevance in the computation, while the most relevant ones lose it. 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. Then, we report on extensive numerical simulations providing evidence of the beneficial noise effects in the neighborhood of the best equalization, often leading to improved generalization.

Figures (12)

• Figure 1: Schematic illustration of the noise analysis proposed in this work. The action of noise on the QNN algorithmic performances can be analyzed via the Quantum Fisher Information Matrix. If noise is too strong, the eigenvalues of the QFIM are exponentially suppressed, which is known to lead to the BPs issue. However, small levels of noise induce an equalization process, in which smaller eigenvalues gain more and more importance, thus allowing a more balanced exploration of the cost landscape. We argue that an optimal level of noise exists, $p^*$, which gives the best equalization and leads to improved generalization performances of the QNN.
• Figure 2: Change in steepness $I_r(\mathbf{x}, \boldsymbol{\theta})$ for the for input $\mathbf{x}$ and parameter vector $\boldsymbol{\theta}$, for an underparametrized QNN of $n=5$ qubits subject to dephasing noise.
• Figure 3: Relative change of the averaged QFIM eigenvalues $\lambda_m$ under different levels of noise $p$ with respect to the noiseless case ($p=0$) for a), d) depolarizing, b), e) dephasing and c), f) amplitude-damping noise. The first row represents the relative change for an underparameterized model ($60$ parameters), while the second for an overparameterized one ($150$ parameters). The average is computed over all the inputs of the training set (noisy sinusoidal dataset) and 5 different parameter vectors.
• Figure 4: Sinusoidal Comparison of optimal noise level $p^*$ obtained from NIE and test MSE on noisy sinusoidal dataset. Columns correspond to different types of noise: depolarizing (DP), phase damping (PD) and amplitude damping (AD). First and second rows refer to the underparameterized model, while third and fourth to the overparameterized one. We can see that $p^*$ estimated with the two methods (vertical lines) are in good agreement.
• Figure 5: Datasets: sinusoidal, sinusoidal 2, diabetes. These are raw data before classical preprocessing.

Theorems & Definitions (2)

• Definition : Best NIE
• Theorem : Adapted from Ref. Khanal2025_data_JSuperC