A question on quantum debugging

As my algorithms class winds down, I've been doing some "topics" lectures, and today I attempted to not make a fool of myself giving students a very high level view of quantum computing, with much help from Dave Bacon and Umesh Vazirani's lecture notes, as well as the Nielsen/Chuang book.

One question came up that I thought was interesting, and I'm hoping that Pontiffs in Shtetls can help answer it :). One of the "features" of programming a randomized algorithm with pseudorandom bits generated by a seed is that you can reproduce a program run by using the same trace. This is of course handy when debugging.

Is there any way of doing this with a quantum algorithm ? I.e is there any way to run a quantum algorithm twice and get the same answer ? maybe using entangled bits in some strange way ?