  We report an experiment to demonstrate a quantum permutation determining
algorithm with linear optical system. By employing photon polarization and
spatial modes, we realize the quantum ququart states and all the essential
permutation transformations. Compared with the classical case, this work
determines the parity of the permutation in only one step of evaluation and
displays the remarkable speedup of quantum algorithm. This experiment is
accomplished in single photon level and exhibits strong universality in quantum
computation.
