Quantum systems have started to emerge as a disruptive technology and enabling platforms - exploiting the principles of quantum mechanics via programmable quantum bits (QuBits) - to achieve quantum supremacy in computing. Academic research, industrial projects (e.g., Amazon Braket, IBM Qiskit), and consortiums like 'Quantum Flagship' are striving to develop practically capable and commercially viable quantum computing (QC) systems and technologies. Quantum Computing as a Service (QCaaS) is viewed as a solution attuned to the philosophy of service-orientation that can offer QC resources and platforms, as utility computing, to individuals and organisations who do not own quantum computers. This research investigates a process-centric and architecture-driven approach to offer a software engineering perspective on enabling QCaaS - a.k.a quantum service-orientation. We employed a two-phase research method comprising (a) a systematic mapping study and (b) an architecture-based development, first to identify the phases of the quantum service development life cycle and subsequently to integrate these phases into a reference architecture that supports QCaaS. The SMS process retrieved a collection of potentially relevant research literature and based on a multi-step selection and qualitative assessment, we selected 41 peer-reviewed studies to answer three RQs. The RQs investigate (i) demographic details in terms of frequency, types, and trends of research, (ii) phases of quantum service development lifecycle to derive a reference architecture for conception, modeling, assembly, and deployment of services, and (iii) The results identify a 4-phased development lifecycle along with quantum significant requirements (QSRs), various modeling notations, catalogue of patterns, programming languages, and deployment platforms that can be integrated in a layered reference architecture to engineer QCaaS.