Quantum computer algorithms are able to solve some problems more efficiently than the best known classical algorithms. For some "black-box" problems, the quantum improvement is provable. Feynman's original idea (in the early 1980's) was to use quantum computers to simulate quantum mechanical systems exponentially more efficiently than the best known classical algorithms. Shor's algorithms solve the integer factorization problem and the discrete logarithm problem, which are at the core of all the widely used public-key cryptosystems. Grover's quantum search algorithm solves a black-box searching problem with quadratically fewer queries than is possible with a classical algorithm. Many more quantum algorithms and algorithmic tools have been developed since these seminal results in the mid-1990's.

I will introduce some of the basic principles and tools behind quantum algorithms, survey some of the main known algorithms, and discuss future directions.