dorsal/arxiv
View SchemaTradeoffs in the Quantum Search Algorithm
| Authors | Lov K. Grover |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201152 |
| URL | https://arxiv.org/abs/quant-ph/0201152 |
| DOI | 10.1103/PhysRevA.66.052314 |
Abstract
Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This has been proved to be the best possible algorithm for the exhuastive search problem in the sense the number of queries it requires cannot be reduced. However, as this paper shows, the number of non-query operations, and thus the total number of operations, can be reduced. The number of non-query unitary operations can be reduced by a factor of log N/alpha*log(log N) while increasing the number of queries by a factor of only (1+(log N)^{-alpha}). Various choices of alpha yield different variants of the algorithm. For example, by choosing alpha to be O(log N/log(log N)), the number of non-query unitary operations can be reduced by 40% while increasing the number of queries by just two.
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"abstract": "Quantum search is a quantum mechanical technique for searching N\npossibilities in only sqrt(N) steps. This has been proved to be the best\npossible algorithm for the exhuastive search problem in the sense the number of\nqueries it requires cannot be reduced. However, as this paper shows, the number\nof non-query operations, and thus the total number of operations, can be\nreduced. The number of non-query unitary operations can be reduced by a factor\nof log N/alpha*log(log N) while increasing the number of queries by a factor of\nonly (1+(log N)^{-alpha}). Various choices of alpha yield different variants of\nthe algorithm. For example, by choosing alpha to be O(log N/log(log N)), the\nnumber of non-query unitary operations can be reduced by 40% while increasing\nthe number of queries by just two.",
"arxiv_id": "quant-ph/0201152",
"authors": [
"Lov K. Grover"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.052314",
"title": "Tradeoffs in the Quantum Search Algorithm",
"url": "https://arxiv.org/abs/quant-ph/0201152"
},
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