  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 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. This is achieved by
defining generalised n-dimensional intrinsic simulation, which brings the
computer science based concepts of simulation and universality closer to
theoretical physics. The result is not only an important simplification of the
QCA model, it also plays a key role in the identification of a minimal
n-dimensional intrinsically universal QCA.
