  We examine the execution of general U(1) transformations on programmable
quantum processors. We show that, with only the minimal assumption of
availability of copies of the one-qubit program state, that the apparent
advantage of existing schemes proposed by G.Vidal it et al. [Phys. Rev. Lett.
88, 047905 (2002)] and M.Hillery et al. [Phys. Rev. A. 65, 022301 (2003)] to
execute a general U(1) transformation with greater probability using complex
program states appears not to hold.
