For some oracular problems, quantum walks provide an exponential speedup over any classical algorithm.

No efficient classical algorithm for computing general discrete logarithms log g is known.

Any comparison-based quantum sorting algorithm would take at least steps, which is already achievable by classical algorithms.

No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, although this is considered unlikely.

What makes quantum algorithms interesting is that they might be able to solve some problems faster than classical algorithms.

Grover's algorithm runs quadratically faster than the best possible classical algorithm for the same task.

The best known classical algorithm for estimating these sums takes exponential time.

It is therefore faster than the classical algorithm, which requires n single-digit products.

The reason is that many classical algorithms are based on (classical) random walks.

Almost everything in that article, that is behind the classical Euclid's algorithm, has been introduced for the need of computer algebra.