Quantum software is an emerging class of software systems, services, and applications that leverage the principles of quantum mechanics through programmable quantum bits (qubits) and quantum gates to perform computations that offer advantages for certain classes of problems. Quantum software architecture enables quantum software developers to abstract away implementation-specific details (i.e., mapping of qubits and quantum gates to high-level architectural components and connectors). Architecture patterns provide proven solutions to recurring design problems, while architecture strategies are approaches that guide the overall design and evolution of a system to meet specific goals. Such patterns and strategies are needed because quantum software systems involve complex hybrid quantum-classical design concerns. However, quantum software practitioners face significant challenges in selecting and implementing appropriate patterns and strategies. To address these challenges, this study proposes decision models for selecting patterns and strategies in six critical design areas in quantum software systems: Communication, Decomposition, Data Processing, Fault Tolerance, Integration and Optimization, and Algorithm Implementation. These decision models are constructed based on data collected from both a mining study (GitHub and Stack Exchange) and an SLR, which were used to identify relevant patterns and strategies with their involved QAs. We then conducted semi-structured interviews with 30 quantum software practitioners to evaluate the familiarity, understandability, completeness, and usefulness of the proposed decision models. The results show that the proposed decision models can aid practitioners in selecting suitable patterns and strategies to address the challenges related to the architecture design of quantum software systems. The dataset is at https://github.com/shamimaaktar1/DMQSA

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