A quantum walk is a time-homogeneous quantum-mechanical process on a graph

defined by analogy to classical random walk. The quantum walker is a particle

that moves from a given vertex to adjacent vertices in quantum superposition.

Here we consider a generalization of quantum walk to systems with more than one

walker. A continuous-time multi-particle quantum walk is generated by a

time-independent Hamiltonian with a term corresponding to a single-particle

quantum walk for each particle, along with an interaction term. Multi-particle

quantum walk includes a broad class of interacting many-body systems such as

the Bose-Hubbard model and systems of fermions or distinguishable particles

with nearest-neighbor interactions. We show that multi-particle quantum walk is

capable of universal quantum computation. Since it is also possible to

efficiently simulate a multi-particle quantum walk of the type we consider

using a universal quantum computer, this model exactly captures the power of

quantum computation. In principle our construction could be used as an

architecture for building a scalable quantum computer with no need for

time-dependent control.