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.

翻译：变分量子算法作为噪声中等规模量子（NISQ）设备的早期应用正日益受到关注。变分方法的主要问题之一在于变分参数优化中出现的贫瘠高原现象。为量子模型添加几何归纳偏置已被提出作为缓解该问题的潜在解决方案，由此催生了名为几何量子机器学习的新领域。本研究引入了一种用于变分量子分类器的等变架构，旨在构建具有$C_4$旋转标签对称性的标签不变图像分类模型。通过将等变电路与两种不同架构进行基准测试，实验观测表明几何方法能够提升模型性能。最终，本文提出一种经典等变卷积运算，用以扩展量子模型处理更大规模图像的能力，同时充分利用NISQ设备的可用资源。