The rise of quantum computing has driven the need for quantum software engineering, yet its programming landscape remains largely unexplored in empirical research. As quantum technologies advance toward industrial adoption, understanding programming aspects is crucial to addressing software development challenges. This study analyzes 6,935 quantum software programming discussion posts from Stack Exchange platforms (Quantum Computing, Stack Overflow, Software Engineering, and Code Review). Using topic modeling and qualitative analysis, we identified key discussion topics, trends (popular and difficult), tools/frameworks, and practitioner challenges. Twenty topics were identified, including popular ones such as physical theories and mathematical foundations, as well as security and encryption algorithms, while the most difficult were object-oriented programming and parameter control in quantum algorithms. Additionally, we identified nine frameworks that support quantum programming, with Qiskit emerging as the most widely adopted. Our findings also reveal core challenges in quantum software programming, thematically mapped into four areas: theories and mathematical concepts, algorithms and applications, experimental practices and software development, and education and community engagement. This study provides empirical insights that can inform future research, tool development, and educational efforts, supporting the evolution of the quantum software ecosystem.