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 experimentally by taking the two-qubit Grover's algorithm implemented in NMR quantum computations, 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.