Quantum Computing is a new paradigm that enables several advances which are impossible using classical technology. With the rise of quantum computers, the software is also invited to change so that it can better fit this new computation way. However, although a lot of research is being conducted in the quantum computing field, it is still scarce studies about the differences of the software and software engineering in this new context. Therefore, this article presents a systematic mapping study to present a wide review on the particularities and characteristics of software that are developed for quantum computers. A total of 24 papers were selected using digital libraries with the objective of answering three research questions elaborated in the conduct of this research.