dorsal/arxiv
View SchemaGrover Algorithm with zero theoretical failure rate
| Authors | G. L. Long |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106071 |
| URL | https://arxiv.org/abs/quant-ph/0106071 |
| DOI | 10.1103/PhysRevA.64.022307 |
| Journal | Phys. Rev. A64 (2001) 022307 |
Abstract
In standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this Letter we present a modified version of Grover's algorithm that searches a marked state with full successful rate. The modification is done by replacing the phase inversion by two phase rotation through angle $\phi$. The rotation angle is given analytically to be $\phi=2 \arcsin(\sin{\pi\over (4J+6)}\over \sin\beta)$, where $\sin\beta={1\over \sqrt{N}}$, $N$ the number of items in the database, and $J$ an integer equal to or greater than the integer part of $({\pi\over 2}-\beta)/(2\beta)$. Upon measurement at $(J+1)$-th iteration, the marked state is obtained with certainty.
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"abstract": "In standard Grover\u0027s algorithm for quantum searching, the probability of\nfinding the marked item is not exactly 1. In this Letter we present a modified\nversion of Grover\u0027s algorithm that searches a marked state with full successful\nrate. The modification is done by replacing the phase inversion by two phase\nrotation through angle $\\phi$. The rotation angle is given analytically to be\n$\\phi=2 \\arcsin(\\sin{\\pi\\over (4J+6)}\\over \\sin\\beta)$, where\n$\\sin\\beta={1\\over \\sqrt{N}}$, $N$ the number of items in the database, and $J$\nan integer equal to or greater than the integer part of $({\\pi\\over\n2}-\\beta)/(2\\beta)$. Upon measurement at $(J+1)$-th iteration, the marked state\nis obtained with certainty.",
"arxiv_id": "quant-ph/0106071",
"authors": [
"G. L. Long"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.64.022307",
"journal_ref": "Phys. Rev. A64 (2001) 022307",
"title": "Grover Algorithm with zero theoretical failure rate",
"url": "https://arxiv.org/abs/quant-ph/0106071"
},
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