Realization of the quantum Toffoli gate with trapped ions
  Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum computation, gates acting on more than two qubits can simplify the implementation of complex quantum algorithms[2]. Thus, a single three-qubit operation can replace a complex sequence of two-qubit gates, which in turn promises faster execution with potentially higher Fidelity. One important three-qubit operation is the quantum Toffoli gate which performs a NOT operation on a target qubit depending on the state of two control qubits. Here we present the first experimental realization of the quantum Toffoli gate in an ion trap quantum computer. Our implementation is particular effcient as we directly encode the relevant logic information in the motion of the ion string. [1] DiVincenzo, D. P. Two-bit gates are universal for quantum computation. cond-mat/9407022, Phys.Rev. A 51, 1015-1022 (1995). [2] Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602-605 (2004). 
T. Monz, K. Kim, W. H\"ansel, M. Riebe, A. Villar, P. Schindler, M.   Chwalla, M. Hennrich, and R. Blatt