Using trapped atomic ions, we demonstrate a tailored and versatile effective spin system suitable for quantum simulations and universal quantum computation.
By microwave control, the sign and effective strength of spin-spin couplings can be changed even during the course of a quantum algorithm. Spins can be selected to serve as quantum memories, not participating in the simultaneously perfomed conditional quantum dynamics of other spins. Using the simultaneous long-range coupling between three spins, we realize a coherent quantum Fourier transform — an essential building block for many quantum algorithms. This approach, using microwave manipulation of the spins only, opens a new route to overcoming technical and physical challenges in the quest for a quantum simulator and a quantum computer.