  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 $N$
with a probability as close to 1 as desired. The algorithm requires $O((\log n
)^3n^3)$ quantum operations, or $O(\log\log n (\log n)^4 n^2)$ operations using
fast multiplication. Verification, quantum optimizations and applications to
RSA and primality tests are also discussed.
