Quantum Manipulation of Trapped Ions in Two Dimensional Coulomb Crystals

Abstract

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.

10 pages, 3 figures. We include an appendix with: (i) Details on the calculation presented in the main text. (ii) An scheme for inducing effective spin-spin interactions with a walking wave scheme for quantum simulations with trapped ions