In this special issue of AIMS Mathematics, it will cover the quantum computing, AI mathematics, and stochastics with applications. Quantum computing will cover the systems, computations, and their mathematics from quantum and statistical mechanics, quantum computers, quantum communications, quantum measurements, and quantum sensors, quantum artificial intelligence (AI) and optimization. AI mathematics will cover general AI models, AI algorithms, and their mathematics. These AI models include AI-native real-world systems from (but not limited to) cloud-computing and communication systems, bioinformatics and biomedical engineering systems, digital and AI token economy. Stochastics will cover diffusion and general stochastic processes, stochastic ordinary and partial differential equations, and their applications in probabilistic big models, statistical machine learning, multimode decision-making neural networks, quantum computing and AI-native systems.