dorsal/arxiv
View SchemaAdiabatic quantum search algorithm for structured problems
| Authors | Jérémie Roland, Nicolas J. Cerf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304039 |
| URL | https://arxiv.org/abs/quant-ph/0304039 |
| DOI | 10.1103/PhysRevA.68.062312 |
| Journal | Phys. Rev. A 68, 062312 (2003). |
Abstract
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speed-up over a classical search, just as Grover's algorithm. In this paper, we study how the structure of the search problem may be exploited to further improve the efficiency of these quantum adiabatic algorithms. We show that by nesting a partial search over a reduced set of variables into a global search, it is possible to devise quantum adiabatic algorithms with a complexity that, although still exponential, grows with a reduced order in the problem size.
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"abstract": "The study of quantum computation has been motivated by the hope of finding\nefficient quantum algorithms for solving classically hard problems. In this\ncontext, quantum algorithms by local adiabatic evolution have been shown to\nsolve an unstructured search problem with a quadratic speed-up over a classical\nsearch, just as Grover\u0027s algorithm. In this paper, we study how the structure\nof the search problem may be exploited to further improve the efficiency of\nthese quantum adiabatic algorithms. We show that by nesting a partial search\nover a reduced set of variables into a global search, it is possible to devise\nquantum adiabatic algorithms with a complexity that, although still\nexponential, grows with a reduced order in the problem size.",
"arxiv_id": "quant-ph/0304039",
"authors": [
"J\u00e9r\u00e9mie Roland",
"Nicolas J. Cerf"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.062312",
"journal_ref": "Phys. Rev. A 68, 062312 (2003).",
"title": "Adiabatic quantum search algorithm for structured problems",
"url": "https://arxiv.org/abs/quant-ph/0304039"
},
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