We present elements of quantum circuits translations from the standard network (or circuit) model to the one-way one. We present a general translation scheme, give an account of currently existing tools to apply the scheme, and propose an extension of those tools into grounds for work towards a complete translation calculus. We analyze the set of difficulties incurred from such work, and show an engendered opening to new sets of discussions and ideas. Among others, this paper extends the findings to the notions of graphical concatenation, graph state reduction (GSR) and graph state extension (GSE) passes. Further, it proposes an algorithm for running the (extended) measurement calculus with acceptable efficiency.
Additional notes: This is a more review-based version of the paper at http://www.cs.indiana.edu/~lvoufo/ow_add_preproc.pdf, which has been submitted to the pre-proceedings of the DCM-QPL'08 workshop (http://www.comlab.ox.ac.uk/people/bob.coecke/DCM_QPL_08.html). An abstract version of it (http://www.cs.indiana.edu/~lvoufo/ow_add_abstract.pdf) has already been accepted for a presentation at the same workshop.
