  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).
