Persistent Homology on near-term Quantum Computers

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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.