Below, is a PDF of the PPP poll. Page down about 5 pages—there’s a list of hypothetical match-ups that narrow the choices to 2, 3, 4, 5 candidates.
Cruz wins them all.
http://www.publicpolicypolling.com/pdf/2015/PPP_Release_IA_121515.pdf
Nice find, but to be fair to Trump, the 55/34 Cruz/Trump head to head poll was just for Iowa. For now...
Please check this again. I looked five pages down and there was no head-to-head date regarding Hillary. I then searched all 88 pages of the pdf for "Hillary" and found 19 hits but not one had anything about a match-up with a Republican. I also noticed that this pdf is only for the Iowa caucus, no averages for national.