  Quantum algorithms are known for providing more efficient solutions to
certain computational tasks than any corresponding classical algorithm. Here we
show that a single qudit is sufficient to implement an oracle based quantum
algorithm, which can solve a black-box problem faster than any classical
algorithm. For $2d$ permutation functions defined on a set of $d$ elements,
deciding whether a given permutation is even or odd, requires evaluation of the
function for at least two elements. We demonstrate that a quantum circuit with
a single qudit can determine the parity of the permutation with only one
evaluation of the function. Our algorithm provides an example for quantum
computation without entanglement since it makes use of the pure state of a
qudit. We also present an experimental realization of the proposed quantum
algorithm with a quadrupolar nuclear magnetic resonance using a single
four-level quantum system, i.e., a ququart.
