Symmetry breaking in geometric quantum machine learning in the presence of noise

Symmetry breaking in geometric quantum machine learning in the presence of noise

17 Jan 2024 | Cenk Tuysuz, Su Yeon Chang, Maria Demidik, Karl Jansen, Sofia Vallecorsa, Michele Grossi
This paper explores the behavior of equivariant quantum neural networks (EQNNs) in the presence of hardware noise, a critical issue that has not been previously studied. The authors investigate the impact of different noise models, such as Pauli channels and amplitude damping (AD) channels, on the equivariance of EQNNs. They find that while certain EQNN models can preserve equivariance under realistic Pauli channels, symmetry breaking occurs under the AD channel. The symmetry breaking is characterized by metrics introduced in the paper, which show that it grows approximately linearly with the number of layers and noise strength. The authors also propose strategies to enhance symmetry protection, such as choosing appropriate representations and adaptive thresholding. Numerical experiments using classical simulators and NISQ hardware support these findings. The paper concludes with a discussion on the implications of these results for the deployment of EQNN models on hardware and suggests future directions for research.This paper explores the behavior of equivariant quantum neural networks (EQNNs) in the presence of hardware noise, a critical issue that has not been previously studied. The authors investigate the impact of different noise models, such as Pauli channels and amplitude damping (AD) channels, on the equivariance of EQNNs. They find that while certain EQNN models can preserve equivariance under realistic Pauli channels, symmetry breaking occurs under the AD channel. The symmetry breaking is characterized by metrics introduced in the paper, which show that it grows approximately linearly with the number of layers and noise strength. The authors also propose strategies to enhance symmetry protection, such as choosing appropriate representations and adaptive thresholding. Numerical experiments using classical simulators and NISQ hardware support these findings. The paper concludes with a discussion on the implications of these results for the deployment of EQNN models on hardware and suggests future directions for research.
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