Geometric quantum machine learning based on equivariant quantum neural
networks (EQNN) recently appeared as a promising direction in quantum machine
learning. Despite the encouraging progress, the studies are still limited to
theory, and the role of hardware noise in EQNN training has never been
explored. This work studies the behavior of EQNN models in the presence of
noise. We show that certain EQNN models can preserve equivariance under Pauli
channels, while this is not possible under the amplitude damping channel. We
claim that the symmetry breaking grows linearly in the number of layers and
noise strength. We support our claims with numerical data from simulations as
well as hardware up to 64 qubits. Furthermore, we provide strategies to enhance
the symmetry protection of EQNN models in the presence of noise.

基于等变量量子神经网络（EQNN）的几何量子机器学习是量子机器学习中的一个有前景的方向，本文研究了 EQNN 模型在噪声存在下的行为，通过数值模拟和高达 64 比特的硬件实验支持实验的结果，并提出了在噪声存在时增强 EQNN 模型对称性保护的策略。