  There have been several non-axiomatic approaches taken to define Quantum
Cellular Automata (QCA). Partitioned QCA (PQCA) are the most canonical of these
non-axiomatic definitions. In this work we first show that any QCA can be put
into the form of a PQCA. Our construction reconciles all the non-axiomatic
definitions of QCA, showing that they can all simulate one another, and hence
that they are all equivalent to the axiomatic definition. Next, we describe a
simple n-dimensional QCA capable of simulating all others, in that the initial
configuration and the forward evolution of any n-dimensional QCA can be encoded
within the initial configuration of the intrinsically universal QCA, and that
several steps of the intrinsically universal QCA then correspond to one step of
the simulated QCA. Both results are made formal by defining generalised
n-dimensional intrinsic simulation, i.e. a notion of simulation which preserves
the topology in the sense that each cell of the simulated QCA is encoded as a
group of adjacent cells in the universal QCA. We argue that this notion brings
the computer science based concepts of simulation and universality one step
closer to theoretical physics.
