dorsal/arxiv
View SchemaA Family of Grover's Quantum Searching Algorithms
| Authors | Alberto Galindo, Miguel A. Martin-Delgado |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0009086 |
| URL | https://arxiv.org/abs/quant-ph/0009086 |
| DOI | 10.1103/PhysRevA.62.062303 |
Abstract
We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the standard Grover's algorithm is a distinguished member of this family. We show that all the algorithms of this class solve the searching problem with an efficiency of order $O(\sqrt{N})$, with a coefficient which is class-dependent. The analysis of this dependence is a test of the stability and robustness of the algorithms. We show the stability of this constructions under perturbations of the initial conditions and extend them upon a very general class of Grover operators.
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"abstract": "We introduce the concepts of Grover operators and Grover kernels to\nsystematically analyse Grover\u0027s searching algorithms. Then, we investigate a\none-parameter family of quantum searching algorithms of Grover\u0027s type and we\nshow that the standard Grover\u0027s algorithm is a distinguished member of this\nfamily. We show that all the algorithms of this class solve the searching\nproblem with an efficiency of order $O(\\sqrt{N})$, with a coefficient which is\nclass-dependent. The analysis of this dependence is a test of the stability and\nrobustness of the algorithms. We show the stability of this constructions under\nperturbations of the initial conditions and extend them upon a very general\nclass of Grover operators.",
"arxiv_id": "quant-ph/0009086",
"authors": [
"Alberto Galindo",
"Miguel A. Martin-Delgado"
],
"categories": [
"quant-ph",
"cond-mat"
],
"doi": "10.1103/PhysRevA.62.062303",
"title": "A Family of Grover\u0027s Quantum Searching Algorithms",
"url": "https://arxiv.org/abs/quant-ph/0009086"
},
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