Both problems are special cases of the abelian hidden subgroup problem, which is now known to have efficient quantum algorithms.
The sequence of gates to be applied is called a quantum algorithm.
There exists an efficient quantum algorithm due to Peter Shor.
Shor's algorithm applies a particular case of this quantum algorithm.
It is also known that quantum algorithms can solve this problem faster in queries.
What makes quantum algorithms interesting is that they might be able to solve some problems faster than classical algorithms.
There are efficient quantum algorithms known for the Abelian hidden subgroup problem.
Efficient quantum algorithms are known for certain non-abelian groups.
Fast quantum algorithms for more complicated formulas are also known.
"It's Galactic binary, sir, a translation program for a quantum algorithm."