  Grover's search algorithm can be applied to a wide range of problems; even
problems not generally regarded as searching problems, can be reformulated to
take advantage of quantum parallelism and entanglement, and lead to algorithms
which show a square root speedup over their classical counterparts.
  In this paper, we discuss a systematic way to formulate such problems and
give as an example a quantum scheduling algorithm for an $R||C_{max}$ problem.
$R||C_{max}$ is representative for a class of scheduling problems whose goal is
to find a schedule with the shortest completion time in an unrelated parallel
machine environment.
  Given a deadline, or a range of deadlines, the algorithm presented in this
paper allows us to determine if a solution to an $R||C_{max}$ problem with $N$
jobs and $M$ machines exists, and if so, it provides the schedule. The time
complexity of the quantum scheduling algorithm is $\mathcal{O}(\sqrt{M^N})$
while the complexity of its classical counterpart is $\mathcal{O}(M^N)$.
