Abstract

Imagine a phone directory containing N names arranged in completely random order. In order to find someone's phone number with a probability of , any classical algorithm (whether deterministic or probabilistic) will need to look at a minimum of names. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only steps. The algorithm is within a small constant factor of the fastest possible quantum mechanical algorithm.