Searching in Grover's Algorithm

1999/01/09 by Richard Jozsa, Jozsa, Richard · 8 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #DNA and Biological Computing #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9901021

8 pages, Latex

arxiv created 1999/01/09 · openalex publication_date 1999/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Grover's algorithm is usually described in terms of the iteration of a compound operator of the form Q = - H I₀ H I_x0. 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.

Cited by

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• Strength and Weakness in Grover's Quantum Search Algorithm
• Constant-Time Quantum Algorithm For The Unstructured Search Problem
• Speedup of iterated quantum search by parallel performance
• An intuitive Hamiltonian for quantum search
• Information and computation: Classical and quantum aspects
• Quantum Search Algorithm with more Reliable Behaviour using Partial Diffusion

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• Grover's Algorithm: Quantum Database Search
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