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This approach allows us to (i) to construct quantum Turing machines (QTM), (ii) to show that any TM can be realized as a QTM, and (iii) to realize a realistic physical machine, namely, a quantum Turing machine (qTM) [@Deutsch91]. We do not focus on the practical implementation of these models. A detailed discussion on the application of these quantum models is given in the next section, where we consider a practical example of a probabilistic realization of a TM-based model.
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