Photonic Quantum Computing and Quantum Topological Data Analysis: A DeepTech Landscape for HealthTech, ClimateTech and FinTech

Abstract: This study investigates the convergence of photonic quantum computing and quantum topological data analysis as an emerging DeepTech pathway for HealthTech, ClimateTech and FinTech. The paper develops a structured literature-review and mathematical framework that connects photonic hardware assumptions, persistent homology, quantum algorithms for topological invariants and commercialization-readiness assessment. The central problem is not whether quantum computing will replace classical analytics in the immediate term, but how a defensible hybrid architecture can identify tasks where topology, optical quantum information processing and sector-specific data geometry create plausible advantage. The research therefore distinguishes near-term value from classical topological machine learning, medium-term value from quantum algorithmic benchmarking and long-term value from fault-tolerant photonic architectures. The method combines documentary evidence from official quantum strategies and peer-reviewed technical literature with a source-calibrated indicator matrix. Public data include national quantum programme commitments and reported photonic quantum projects, while coded sector indicators represent data intensity, photonic fit, QTDA relevance, infrastructure readiness, regulatory maturity, commercial pull and governance burden. Mathematical support is provided through equations for quantum state representation, Vietoris-Rips filtrations, persistent Betti numbers, persistence landscapes and a weighted readiness index. Results indicate that FinTech shows the strongest near-term operational readiness for topological early-warning systems, HealthTech offers the deepest scientific and clinical transformation potential, and ClimateTech provides the clearest public-value use case through explainable anomaly detection, carbon monitoring and resilience planning. The paper concludes that commercialization should proceed through staged validation, with classical TDA as the immediate baseline, quantum algorithms as verifiable benchmark objects and photonic quantum computing as a strategic, fault-tolerant horizon. Keywords: photonic quantum computing; quantum topological data analysis; persistent homology; DeepTech commercialization; HealthTech; ClimateTech; FinTech; quantum algorithms; topological machine learning; innovation governance.