Identity circuits are the basis for rewriting rules in the process of optimizing reversible and quantum circuits. Rewriting rules are also known as templates. It has been shown that templates can play an important role in optimizing quantum circuits. This paper presents an in-depth study of the properties of such templates. It is shown that all optimal realizations, within certain limitations, are embedded in templates. The properties presented here, lead to a systematic method of generating all templates with a given number of lines. It is proven that, if the complete set of templates is available, template matching results in optimal circuits. © 2013 Springer-Verlag Berlin Heidelberg.
Rahman, M. M., & Dueck, G. W. (2013). Properties of quantum templates. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7581 LNCS, pp. 125–137). Springer Verlag. https://doi.org/10.1007/978-3-642-36315-3_10