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。

存在噪声下的几何量子机器学习中的对称性破缺

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

Real-world grasp detection is challenging due to the stochasticity in grasp
dynamics and the noise in hardware. Ideally, the system would adapt to the real
world by training directly on physical systems. However, this is generally
difficult due to the large amount of training data required by most grasp
learning models. In this paper, we note that the planar grasp function is
$\SE(2)$-equivariant and demonstrate that this structure can be used to
constrain the neural network used during learning. This creates an inductive
bias that can significantly improve the sample efficiency of grasp learning and
enable end-to-end training from scratch on a physical robot with as few as
$600$ grasp attempts. We call this method Symmetric Grasp learning (SymGrasp)
and show that it can learn to grasp ``from scratch'' in less that 1.5 hours of
physical robot time.

该研究提出一种称为 Symmetric Grasp learning 的方法，可以实现端到端训练，在硬件噪声和抓取动态难以处理的情况下，仅进行不到 600 次尝试即可从零开始学习抓取任务。