Quantum Mechanics Helps in Searching for a Needle in a Haystack

Quantum mechanics can speed up a range of search applications over unsorted data by properly adjusting the phases of various operations, and successful computations reinforce each other while others interfere randomly.

Abstract

Quantum mechanics can speed up a range of search applications over unsorted data. For example, imagine a phone directory containing $N$ names arranged in completely random order. To find someone's phone number with a probability of 50%, any classical algorithm (whether deterministic or probabilistic) will need to access the database a minimum of $0.5N$ times. 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 $O(\sqrt{N})$ accesses to the database.