  Atomic systems in regular lattices are intriguing systems for implementing
ideas in quantum simulation and information processing. Focusing on laser
cooled ions forming Wigner crystals in Penning traps, we find a robust and
simple approach to engineering non-trivial 2-body interactions sufficient for
universal quantum computation. We then consider extensions of our approach to
the fast generation of large cluster states, and a non-local architecture using
an asymmetric entanglement generation procedure between a Penning trap system
and well-established linear Paul trap designs.
