Let me first mention a recent paper on quantum computing in the Bohm interpretation - http://arxiv.org/abs/1205.2563 , FWIW, though I cannot offer any comments on it right now, sorry.
Another thing. As nightlight noticed in his posts on hidden variables, there is an off-the-shelf mathematical trick (an extension of the Carleman linearization) that embeds a system of partial differential equations into a quantum field theory (see, e.g., my article in Int'l Journ. of Quantum Information ( akhmeteli.org/akh-prepr-ws-ijqi2.pdf ), the end of Section 3, and references there. There is also a substantially updated version at arxiv.org/abs/1111.4630).
nightlight also mentioned what that may mean for quantum computing. One can imagine a situation where Nature is described correctly by a quantum field theory (QFT), whereas actually only a limited subset of the entire set of states of the QFT is realized in Nature, the subset that is correctly described by a (classical) system of partial differential equations, so there are obvious limitations on how fast quantum computing can be. Of course this is highly hypothetical, but perhaps quite relevant to the question above on the relation between quantum computing and foundations of quantum theory.