Effects of noise on the overparametrization of quantum neural networks

Overparametrization is one of the most surprising and notorious phenomena in machine learning. Recently, there have been several efforts to study if, and how, quantum neural networks (QNNs) acting in the absence of hardware noise can be overparametrized. In particular, it has been proposed that a QN...

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Bibliographic Details
Published in:Physical review research Vol. 6; no. 1; p. 013295
Main Authors: García-Martín, Diego, Larocca, Martín, Cerezo, M.
Format: Journal Article
Language:English
Published: United States American Physical Society (APS) 18.03.2024
American Physical Society
Subjects:
machine learning
MATHEMATICS AND COMPUTING
quantum algorithms & computation
quantum information processing
quantum information theory
quantum metrology
quantum parameter estimation
ISSN:2643-1564, 2643-1564
Online Access:Get full text
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Summary:Overparametrization is one of the most surprising and notorious phenomena in machine learning. Recently, there have been several efforts to study if, and how, quantum neural networks (QNNs) acting in the absence of hardware noise can be overparametrized. In particular, it has been proposed that a QNN can be defined as overparametrized if it has enough parameters to explore all available directions in state space. That is, if the rank of the quantum Fisher information matrix (QFIM) for the QNN's output state is saturated. Here, we explore how the presence of noise affects the overparametrization phenomenon. Our results show that noise can “turn on” previously zero eigenvalues of the QFIM. This enables the parametrized state to explore directions that were otherwise inaccessible, thus potentially turning an overparametrized QNN into an underparametrized one. For small noise levels, the QNN is quasioverparametrized, as large eigenvalues coexists with small ones. Then, we prove that as the magnitude of noise increases all the eigenvalues of the QFIM become exponentially suppressed, indicating that the state becomes insensitive to any change in the parameters. As such, there is a pull-and-tug effect where noise can enable new directions but also suppress the sensitivity to parameter updates. Finally, our results imply that current QNN capacity measures are ill-defined when hardware noise is present.
Bibliography:89233218CNA000001; 20230049DR; 20230527ECR
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
USDOE Laboratory Directed Research and Development (LDRD) Program
LA-UR-22-33019
USDOE National Nuclear Security Administration (NNSA)
ISSN:2643-1564
2643-1564
DOI:10.1103/PhysRevResearch.6.013295