Variational quantum algorithms are gaining attention as an early application
of Noisy Intermediate-Scale Quantum (NISQ) devices. One of the main problems of
variational methods lies in the phenomenon of Barren Plateaus, present in the
optimization of variational parameters. Adding geometric inductive bias to the
quantum models has been proposed as a potential solution to mitigate this
problem, leading to a new field called Geometric Quantum Machine Learning. In
this work, an equivariant architecture for variational quantum classifiers is
introduced to create a label-invariant model for image classification with
$C_4$ rotational label symmetry. The equivariant circuit is benchmarked against
two different architectures, and it is experimentally observed that the
geometric approach boosts the model's performance. Finally, a classical
equivariant convolution operation is proposed to extend the quantum model for
the processing of larger images, employing the resources available in NISQ
devices.

引入了一种等变结构的变分量子分类器，用于具有 $C_4$ 旋转标签对称性的图像分类，实验证明了等变的方法能够提升模型性能，最后还提出了一种经典等变卷积操作用于处理更大的图像。

旋转不变的变分量子电路图像分类

Image Classification with Rotation-Invariant Variational Quantum  Circuits

We introduce a novel architecture for graph networks which is equivariant to
any transformation in the coordinate embeddings that preserves the distance
between neighbouring nodes. In particular, it is equivariant to the Euclidean
and conformal orthogonal groups in $n$-dimensions. Thanks to its equivariance
properties, the proposed model is extremely more data efficient with respect to
classical graph architectures and also intrinsically equipped with a better
inductive bias. We show that, learning on a minimal amount of data, the
architecture we propose can perfectly generalise to unseen data in a synthetic
problem, while much more training data are required from a standard model to
reach comparable performance.

通过引入一种新颖的图网络架构，它对于保持相邻节点距离的所有坐标嵌入的任何变换都具有等变性，特别是在 $n$- 维中具有欧几里得和共形正交群等变性，从而使得所提出的模型相对于传统图形架构更加数据高效，并且本质上配备了更好的归纳偏差。我们表明，通过少量数据的学习，我们提出的架构可以完全推广到合成问题中的未见数据，而标准模型需要更多的训练数据才能达到可比较的性能。

基于等变性的图网络数据效率

Data efficiency in graph networks through equivariance

We present a neural network architecture that is fully equivariant with
respect to transformations under the Lorentz group, a fundamental symmetry of
space and time in physics. The architecture is based on the theory of the
finite-dimensional representations of the Lorentz group and the equivariant
nonlinearity involves the tensor product. For classification tasks in particle
physics, we demonstrate that such an equivariant architecture leads to
drastically simpler models that have relatively few learnable parameters and
are much more physically interpretable than leading approaches that use CNNs
and point cloud approaches. The competitive performance of the network is
demonstrated on a public classification dataset [27] for tagging top quark
decays given energy-momenta of jet constituents produced in proton-proton
collisions.

本文介绍一种基于洛伦兹群的有等变性的神经网络体系结构，其用于分类任务在粒子物理学中表现出的结果优于卷积神经网络和点云方法。