Utilising quantum computing technology to enhance artificial intelligence systems is expected to improve training and inference times, increase robustness against noise and adversarial attacks, and reduce the number of parameters without compromising accuracy. However, moving beyond proof-of-concept or simulations to develop practical applications of these systems while ensuring high software quality faces significant challenges due to the limitations of quantum hardware and the underdeveloped knowledge base in software engineering for such systems. In this work, we have conducted a systematic mapping study to identify the challenges and solutions associated with the software architecture of quantum-enhanced artificial intelligence systems. The results of the systematic mapping study reveal several architectural patterns that describe how quantum components can be integrated into inference engines, as well as middleware patterns that facilitate communication between classical and quantum components. Each pattern realises a trade-off between various software quality attributes, such as efficiency, scalability, trainability, simplicity, portability, and deployability. The outcomes of this work have been compiled into a catalogue of architectural patterns.