  Quantum systems have started to emerge as a disruptive technology and
enabling platforms - exploiting the principles of quantum mechanics - to
achieve quantum supremacy in computing. Academic research, industrial projects
(e.g., Amazon Braket), 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. To understand the quantum service development
life cycle and pinpoint emerging trends, we used evidence-based software
engineering approach to conduct a systematic mapping study (SMS) of research
that enables or enhances QCaaS. The SMS process retrieved a total of 55
studies, and based on their qualitative assessment we selected 9 of them to
investigate (i) the functional aspects, design models, patterns, programming
languages, deployment platforms, and (ii) trends of emerging research on QCaaS.
The results indicate three modelling notations and a catalogue of five design
patterns to architect QCaaS, whereas Python (native code or frameworks) and
Amazon Braket are the predominant solutions to implement and deploy QCaaS
solutions. From the quantum software engineering (QSE) perspective, this SMS
provides empirically grounded findings that could help derive processes,
patterns, and reference architectures to engineer software services for QC.
