dorsal/arxiv
View SchemaA Generalization of Grover's Algorithm
| Authors | Luigi Accardi, Ruben Sabbadini |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0012143 |
| URL | https://arxiv.org/abs/quant-ph/0012143 |
Abstract
We investigate the necessary and sufficient conditions in order that a unitary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expense of the other components. This leads to a general method which allows, given a vector and one of its components we want to amplify, to choose the optimal unitary operator which realizes that goal. Grover's quantum algorithm is shown to be a particular case of our general method. However the general structure of the unitary we find is remarkably similar to that of Grover's one: a sign flip of one component combined with a reflection with respect to a vector. In Grover's case this vector is fixed; in our case it depends on a parameter and this allows optimization.
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"abstract": "We investigate the necessary and sufficient conditions in order that a\nunitary operator can amplify a pre-assigned component relative to a particular\nbasis of a generic vector at the expense of the other components. This leads to\na general method which allows, given a vector and one of its components we want\nto amplify, to choose the optimal unitary operator which realizes that goal.\nGrover\u0027s quantum algorithm is shown to be a particular case of our general\nmethod. However the general structure of the unitary we find is remarkably\nsimilar to that of Grover\u0027s one: a sign flip of one component combined with a\nreflection with respect to a vector. In Grover\u0027s case this vector is fixed; in\nour case it depends on a parameter and this allows optimization.",
"arxiv_id": "quant-ph/0012143",
"authors": [
"Luigi Accardi",
"Ruben Sabbadini"
],
"categories": [
"quant-ph"
],
"title": "A Generalization of Grover\u0027s Algorithm",
"url": "https://arxiv.org/abs/quant-ph/0012143"
},
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