Abstract
Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the Carmichael function for any integer with a probability as close to 1 as desired. The algorithm requires $O((\log n )^3n^3)O(\log\log n (\log n)^4 n^2)$ operations using fast multiplication. Verification, quantum optimizations and applications to RSA and primality tests are also discussed.