You do not mention Peter Shor's algorithm that finds the prime factors of an integer using a quantum computer. It is a compelling example because it is much faster than most efficient known factoring algorithm using a classical computer.

You do mention Shor's algorithm in your book, but I think you should mention it here because it is the most compelling application of a quantum computer.

Factorization is not NP-hard like the traveling Salesman Problem, but it is thought to be difficult. People might be tempted to believe that a quick algorithm for factorization must somehow exploit computation in many worlds.