Abstract:
In this note we present two natural algorithms—one for sorting, and another
for searching a sorted list of items. Both algorithms work in O(√N) time, N being
the size of the list. A combination of these algorithms can search an unsorted list
in O(√N) time, an impossibility for classical algorithms. The same complexity is
achieved by Grover’s quantum search algorithm; in contrast to Grover’s algorithm
which is probabilistic, our method is guaranteed correct. Two applications will
conclude this note.