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Quantum computers can search rapidly by using almost any transformation

Lov K. Grover
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Abstract

A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation called the Walsh-Hadamard (W-H) transform. This paper shows that this algorithm can be implemented by replacing the W-H transform by almost any quantum mechanical operation. This leads to several new applications where it improves the number of steps by a square-root. It also broadens the scope for implementation since it demonstrates quantum mechanical algorithms that can readily adapt to available technology.

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Lov K. Grover. 1997-12-03. Quantum computers can search rapidly by using almost any transformation. https://doi.org/10.1103/physrevlett.80.4329

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