  Quantum algorithms are known for presenting more efficient solutions to
certain computational tasks than any corresponding classical algorithm. It has
been thought that the origin of the power of quantum computation has its roots
in non-classical correlations such as entanglement or quantum discord. However,
it has been recently shown that even a single pure qudit is sufficient to
design an oracle-based algorithm which solves a black-box problem faster than
any classical approach to the same problem. In particular, the algorithm that
we consider determines whether eight permutation functions defined on a set of
four elements is positive or negative cyclic. While any classical solution to
this problem requires two evaluations of the function, quantum mechanics allows
us to perform the same task with only a single evaluation. Here, we present the
first experimental demonstration of the considered quantum algorithm with a
quadrupolar nuclear magnetic resonance setup using a single four-level quantum
system, i.e., a ququart.
