Demonstrating quantum algorithm acceleration with NMR quantum computer
  In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger modules, such that the desired unitary matrix expressing the algorithm is directly implemented. We demonstrate this by taking the two-qubit Grover's algorithm implemented in NMR quantum computation, whose pseudopure state is generated by cyclic permutations of the state populations. This is the first exact time-optimal solution, to our knowledge, obtained for a self-contained quantum algorithm. 
Mikio Nakahara, Yasushi Kondo, Kazuya Hata, Shogo Tanimura