Searching in Grover's Algorithm

Richard Jozsa

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Searching in Grover's Algorithm

Richard Jozsa

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Abstract

Grover's algorithm is usually described in terms of the iteration of a compound operator of the form $Q = - H I_{0} H I_{x_0}$. Although it is quite straightforward to verify the algebra of the iteration, this gives little insight into why the algorithm works. What is the significance of the compound structure of $Q$? Why is there a minus sign? Later it was discovered that $H$ could be replaced by essentially any unitary $U$. What is the freedom involved here? We give a description of Grover's algorithm which provides some clarification of these questions.

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Richard Jozsa. 1999-01-09. Searching in Grover's Algorithm. https://arxiv.org/abs/quant-ph/9901021

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