Quantum gates with hot trapped ions

Summary form only given.In several applications of quantum communication and computation, one has to be able to perform some operations between two-level systems (qubits). For example, any quantum algorithm involves quantum gates between several qubits; in teleportation, one has to perform joint measurements between two qubits; in order to purify states, one also needs these operations. We previously proposed a way to implement these operations for a set of ions confined in a trap at zero temperature. It was based in the selective excitation of the center of mass mode of the collective motion using laser light, such that only when two atoms are in a given state, this state changes. In this contribution, we propose a different scheme to perform quantum gates between two ions in a trap. The most remarkable difference from our previous proposal is that the present one does not need to have the ions cooled to the ground state of the motional potential. It also operates in a time scale comparable to the oscillation frequency of the trap. On the other hand, it cannot be easily scaled up to include the presence of many ions, and therefore it does not represent an implementation of a quantum computer. The scheme is based on the interaction of the ions with laser fields, so that depending on the internal state of one ion, the other ion suffers a displacement in opposite directions. A laser with a space-dependent profile induces then a different rotation in the second ion, depending on its position. We study the conditions under which one can obtain optimal results, as well as the sensitivity to imperfections.