This paper provides a comprehensive review of the emerging field of quantum robotics and its potential applications in space exploration and astrobiology. The current state-of-the-art in quantum robotics is discussed, including key capabilities enabled by the integration of quantum computing and quantum sensing with robotics. Potential uses of quantum robots for autonomous exploration, biomolecule and biomarker detection, chemical and biological simulations, and navigation in extraterrestrial environments are explored. Technical challenges such as dealing with space radiation, thermal regulation, power requirements, reliability, and communication networks are examined. Current and future space missions that could benefit from quantum robots, such as Mars rovers, exoplanet searches, and sample return missions, are discussed through case studies. The future outlook and prospects of quantum robotics in transforming space exploration and astrobiology through improved efficiency, accuracy, and autonomous operations are highlighted.