Persistent Homology on near-term Quantum Computers

公平、信任和透明度是阻碍人工智能在关键应用领域广泛采用的主要问题。人们发现人工智能系统在许多情况下会产生不公平、有偏见和不道德的决定。可解释性是理解模型预测背后原因的一种方法，可以帮助确保模型公平对待所有用户。可解释人工智能（XAI）领域专注于开发工具、框架和方法，以帮助理解机器学习模型如何做出决策。拓扑数据分析（TDA）是数据科学的一个新兴领域，旨在利用数据的形状来表征数据。它是可解释人工智能的使能技术之一。TDA提取拓扑特征来捕获复杂数据集的多尺度、全局和内在属性。它的应用范围涵盖金融、生物、神经科学、计算机视觉和文本分析等所有垂直行业。持久同源性（Persistent Homology， PH）是TDA的核心，它是一种将噪声和高维数据集的拓扑特征总结为直观、可解释和低维表示的有用方法。然而，在商业应用程序中使用TDA/Persistent Homology经常受到精确计算拓扑描述符所需的计算复杂性的阻碍。我们的项目将研究适用于近期量子硬件的持久同源技术的实现，以便建立与硬件发展相一致的商业部署路线图。我们利用量子计算算法和硬件可用性的最新进展，从高维大数据集中提取拓扑特征。

Fairness, trust, and transparency are the primary concerns hindering the wider adoption of AI in critical application domains. AI systems have been found to produce unfair, biased, and unethical decisions in many instances. Explainability is one way to understand the reasons behind a model's predictions can help ensure models are treating all users fairly. The field of Explainable AI (XAI) is focused on developing tools, frameworks, and methods that help understand how machine learning models make decisions.Topological Data Analysis (TDA) is an nascent field of data science that aims at characterizing data using its shape. It is one of the enabling technologies for Explainable AI. TDA extracts topological features to capture multi-scale, global, and intrinsic properties of complex data sets. It has applications across all the industry verticals ranging from finance, biology, neuroscience, computer vision and text analytics.Persistent Homology (PH), the workhorse of TDA, is a useful way to summarise the topological characteristics of noisy and high dimensional datasets as an intuitive, interpretable and lower dimensional representation. However, the use of TDA/Persistent Homology in commercial applications is often hindered by the computational complexity required to compute topological descriptors exactly.Our project will study the implementation of persistent homology techniques suitable for near-term quantum hardware in order to establish commercial deployment roadmap aligned with hardware developments. We take advantage of recent advancements in quantum computing algorithms and hardware availability to extract topological features from high dimensional big datasets.