  Quantum computation has attracted much attention since it was shown by Shor
and Grover the possibility to implement quantum algorithms able to realize,
respectively, factoring and searching in a faster way than any other known
classical algorithm. It is possible to use Grover algorithm, taking profit of
its ability to find a specific value in a unordered database, to find, for
example, the zero of a logical function; the minimal or maximal value in a
database or to recognize if an odd number is prime or not. Here we show quantum
algorithms to solve those cited mathematical problems. The solution requires
the use of a quantum bit string comparator being used as oracle. This quantum
circuit compares two quantum states and identifies if they are equal or,
otherwise, which of them is the largest. Moreover, we also show the quantum bit
string comparator allow us to implement conditional statements in quantum
computation, a fundamental structure for designing of algorithms.
