  We show that a large number of ions stored in a Penning trap, and forming a
2D Coulomb crystal, provides an almost ideal system for scalable quantum
computation and quantum simulation. In particular, the coupling of the internal
states to the motion of the ions transverse to the crystal plane, allows one to
implement two qubit quantum gates. We analyze in detail the decoherence induced
by anharmonic couplings with in--plane hot vibrational modes, and show that
very high gate fidelities can be achieved with current experimental set--ups.
