dorsal/arxiv
View SchemaA Quantum Random Walk Search Algorithm
| Authors | Neil Shenvi, Julia Kempe, K. Birgitta Whaley |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210064 |
| URL | https://arxiv.org/abs/quant-ph/0210064 |
| DOI | 10.1103/PhysRevA.67.052307 |
| Journal | Phys. Rev. A, Vol. 67 (5), 052307 (2003) |
Abstract
Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speed-up over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random walk architecture that provides such a speed-up. It will be shown that this algorithm performs an oracle search on a database of $N$ items with $O(\sqrt{N})$ calls to the oracle, yielding a speed-up similar to other quantum search algorithms. It appears that the quantum random walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms.
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"abstract": "Quantum random walks on graphs have been shown to display many interesting\nproperties, including exponentially fast hitting times when compared with their\nclassical counterparts. However, it is still unclear how to use these novel\nproperties to gain an algorithmic speed-up over classical algorithms. In this\npaper, we present a quantum search algorithm based on the quantum random walk\narchitecture that provides such a speed-up. It will be shown that this\nalgorithm performs an oracle search on a database of $N$ items with\n$O(\\sqrt{N})$ calls to the oracle, yielding a speed-up similar to other quantum\nsearch algorithms. It appears that the quantum random walk formulation has\nconsiderable flexibility, presenting interesting opportunities for development\nof other, possibly novel quantum algorithms.",
"arxiv_id": "quant-ph/0210064",
"authors": [
"Neil Shenvi",
"Julia Kempe",
"K. Birgitta Whaley"
],
"categories": [
"quant-ph",
"cs.DS"
],
"doi": "10.1103/PhysRevA.67.052307",
"journal_ref": "Phys. Rev. A, Vol. 67 (5), 052307 (2003)",
"title": "A Quantum Random Walk Search Algorithm",
"url": "https://arxiv.org/abs/quant-ph/0210064"
},
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