  Using trapped atomic ions we demonstrate a tailored and versatile effective
spin-system suitable for quantum simulations and universal quantum computation.
By simply applying microwave pulses, selected spins can be decoupled from the
remaining system and thus can serve as a quantum memory, while simultaneously,
other coupled spins perform conditional quantum dynamics. Also, microwave
pulses can change the sign of spin-spin couplings, as well as their effective
strength, even during the course of a quantum algorithm. Taking advantage of
the simultaneous long-range coupling between three spins a coherent quantum
Fourier transform -- an essential building block for many quantum algorithms --
is efficiently realized. This approach, which is based on microwave-driven
trapped ions and is complementary to laser-based methods, opens a new route to
overcoming technical and physical challenges in the quest for a quantum
simulator and a quantum computer.
