dorsal/arxiv
View SchemaSolving the quantum search problem in polynomial time on an NMR quantum computer
| Authors | Xijia Miao |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206102 |
| URL | https://arxiv.org/abs/quant-ph/0206102 |
Abstract
The quantum search problem is an important problem due to the fact that a general NP problem can be solved efficiently by an unsorted quantum search algorithm. Here it has been shown that the quantum search problem could be solved in polynomial time on an NMR quantum computer. The NMR ensemble quantum computation is based on the quantum mechanical unitary dynamics that both a closed quantum system and its ensemble obey the same quantum mechanical unitary dynamics instead of on the pseudopure state or the effective pure state of the classical NMR quantum computation. Based on the new principle the conventional NMR multiple-quantum spectroscopy has been developed to solve experimentally the search problem. The solution information of the search problem is first loaded on the unitary evolution propagator which is constructed with the oracle unitary operation and oracle-independent unitary operations and is used to excite the multiple-quantum coherence in a spin ensemble. Then the multiple- quantum spectroscopy is used to extract experimentally the solution information. It has been discussed how to enhance the output NMR signal of the quantum search NMR multiple-quantum pulse sequence and some approaches to enhancing the NMR signal are also proposed. The present work could be helpful for conventional high field NMR machines to solve efficiently the quantum search problem.
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"abstract": "The quantum search problem is an important problem due to the fact that a\ngeneral NP problem can be solved efficiently by an unsorted quantum search\nalgorithm. Here it has been shown that the quantum search problem could be\nsolved in polynomial time on an NMR quantum computer. The NMR ensemble quantum\ncomputation is based on the quantum mechanical unitary dynamics that both a\nclosed quantum system and its ensemble obey the same quantum mechanical unitary\ndynamics instead of on the pseudopure state or the effective pure state of the\nclassical NMR quantum computation. Based on the new principle the conventional\nNMR multiple-quantum spectroscopy has been developed to solve experimentally\nthe search problem. The solution information of the search problem is first\nloaded on the unitary evolution propagator which is constructed with the oracle\nunitary operation and oracle-independent unitary operations and is used to\nexcite the multiple-quantum coherence in a spin ensemble. Then the multiple-\nquantum spectroscopy is used to extract experimentally the solution\ninformation. It has been discussed how to enhance the output NMR signal of the\nquantum search NMR multiple-quantum pulse sequence and some approaches to\nenhancing the NMR signal are also proposed. The present work could be helpful\nfor conventional high field NMR machines to solve efficiently the quantum\nsearch problem.",
"arxiv_id": "quant-ph/0206102",
"authors": [
"Xijia Miao"
],
"categories": [
"quant-ph"
],
"title": "Solving the quantum search problem in polynomial time on an NMR quantum computer",
"url": "https://arxiv.org/abs/quant-ph/0206102"
},
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