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Quantum Mechanics helps in searching for a needle in a haystack

Lov K. Grover
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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 O(N) 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.

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Lov K. Grover. 1997-07-17. Quantum Mechanics helps in searching for a needle in a haystack. https://doi.org/10.1103/physrevlett.79.325

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