标题： 基于几何的量子机器学习能否在条形码分类中带来优势？ 显示英文标题

标题： Can Geometric Quantum Machine Learning Lead to Advantage in Barcode Classification?

摘要： 我们考虑区分两个向量（可视化为图像或条形码）并学习它们是否相关的问题。 为此，我们开发了一种具有嵌入对称性的几何量子机器学习（GQML）方法，该方法允许根据全局相关性对相似和不相似对进行分类，并能够仅从少量样本中进行泛化。 与迄今为止开发的GQML算法不同，我们提出关注对称性感知的测量适应，其性能优于单位参数化。 我们将用于相似性测试的GQML与经典的深度神经网络和具有Siamese结构的卷积神经网络进行比较。 我们表明，量子网络大大优于其经典对应物。 我们通过分析用于组成数据集的相关分布来解释这种性能差异。 我们将相似性测试与展示BQP复杂度类和多项式层次结构之间已证明最大分离的问题联系起来。 虽然实现优势的能力在很大程度上取决于数据加载方式，但我们讨论了类似问题如何可以从量子机器学习中受益。 显示英文摘要

摘要： We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries that allows for the classification of similar and dissimilar pairs based on global correlations, and enables generalization from just a few samples. Unlike GQML algorithms developed to date, we propose to focus on symmetry-aware measurement adaptation that outperforms unitary parametrizations. We compare GQML for similarity testing against classical deep neural networks and convolutional neural networks with Siamese architectures. We show that quantum networks largely outperform their classical counterparts. We explain this difference in performance by analyzing correlated distributions used for composing our dataset. We relate the similarity testing with problems that showcase a proven maximal separation between the BQP complexity class and the polynomial hierarchy. While the ability to achieve advantage largely depends on how data are loaded, we discuss how similar problems can benefit from quantum machine learning.