We present a semantic model for quantum programming language QML, which incorporates computational reversibility for classical and quantum data and control, omitting measurements. From the language, its syntax and typing rules are retaken, and operationally it is not conceived with quantum circuits, but by a semantics given by functions. We show an extension of the language, where inverse functions are defined, which are incorporated into the semantics generating a history track with the operations executed given any program. The rules for executing reversibility are also added and depend on the final value of a program. Then, it contributes to the study of reversibility in programming languages; and such that in quantum nature such property must be satisfied, in this language, how it is conceived and considering that there is still no quantum computer in which it can be implemented, this history and the inverse functions are not trivial and allow us to determine that this language is reversible.