Efficient implementations of the Quantum Fourier Transform: an   experimental perspective
  The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the implementation. We focus here on an interesting decomposition of the QFT as a product of the non-selective Hadamard transformation followed by multiqubit gates corresponding to square- and higher-roots of controlled-NOT gates. This decomposition requires only O(n) operations and is thus linear in the number of qubits $n$. The schemes were implemented on a two-qubit NMR quantum information processor and the resultant density matrices reconstructed using standard quantum state tomography techniques. Their experimental fidelities have been measured and compared. 
Kavita Dorai and Dieter Suter (Department of Physics, University of   Dortmund, Germany)