[en] A modified ion trap is described where experiments (in particular related to quantum information processing) that usually require optical radiation can be carried out using microwave or radio frequency electromagnetic fields. Instead of applying the usual methods for coherent manipulation of trapped ions, a string of ions in such a modified trap can be treated like a molecule in nuclear magnetic resonance experiments taking advantage of spin-spin coupling. The collection of trapped ions can be viewed as an N-qubit molecule with adjustable spin-spin coupling constants. Given N identically prepared quantum mechanical two-level systems (qubits), the optimal strategy to estimate their quantum state requires collective measurements. Using the ground state hyperfine levels of electrodynamically trapped ¹⁷¹Yb⁺, we have implemented an adaptive algorithm for state estimation involving sequential measurements on arbitrary qubit states