In pilot wave theory where is the wave? As a non specialist, for a single particle system it's easy to appreciate the concept of a pilot wave extending through all Euclidean space, guiding a particle which ends up at a location determined by the pilot wave and its initial location.
For multiple particles however the wave would presumably need more dimensions to reflect the configuration space of the system.
Is this correct, and if so where does the pilot wave reside? 
A related question may be, if quantum computers give an exponential speedup for factorization, then according to pilot wave theory where does the computation take place? 
 A: The "pilot wave" is just the usual wave function of quantum mechanics. 
If you have $N$ spinless particles, it is a map: $\psi: \mathbb{R}^{3N} \to \mathbb{C}$. This means it lives in the 3N-dimensional configuration space of the particles. I should emphasize that this is not a specialty of pilot wave theory but just the usual framework of quantum mechanics.
The special thing in pilot wave theory are the additional actual particles that actually have positions in $\mathbb{R}^3$ and thus link the abstract object $\psi$ with objects that can be thought of as moving in our physical world, as the objects that tables, chairs and people are made of.
I don't totally understand the intent of your last question, but let's try: The obvious answer is that if a computer computes something, this computation takes place inside of the computer. You know, configuration space is not really a "place" in any reasonable sense. It's an abstract mathematical way of describing the things that happen when, e.g. in a quantum computer, particles move back and forth.
