1999/03/23 by Sixia Yu, Yu, Sixia, Chang-Pu Sun +1 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9903075
11 Pages; RevTex
arxiv created 1999/03/23 · openalex publication_date 1999/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The search operation for a marked state by means of Grover's quantum searching algorithm is shown to be an element of group SU(2) which acts on a 2-dimensional space spanned by the marked state and the unmarked collective state. Based on this underlying structure, those exact bounds of the steps in various quantum search algorithms are obtained in a quite concise way. This reformulation of the quantum searching algorithm also enables a detailed analysis of the decoherence effects caused by its coupling with an environment. It turns out that the environment will not only make the quantum search invalid in case of complete decoherence, where the probability of finding the marked state is unchanged, but also it may make the quantum search algorithm worse than expected: It will decrease this probability when the environment shows its quantum feature.