dorsal/arxiv
View SchemaQuantum search of partially ordered sets
| Authors | Ashley Montanaro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702196 |
| URL | https://arxiv.org/abs/quant-ph/0702196 |
| Journal | Quantum Information & Computation, vol. 9, no. 7&8, pp. 0628-0647, 2009 |
Abstract
We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can achieve at most a quadratic improvement in query complexity over classical algorithms, up to logarithmic factors; we also give quantum algorithms that almost achieve this optimal reduction in complexity. In one model, we give an improved quantum algorithm for searching forest-like posets; in the other, we give an optimal O(sqrt(m))-query quantum algorithm for searching posets derived from m*m arrays sorted by rows and columns. This leads to a quantum algorithm that finds the intersection of two sorted lists of n integers in O(sqrt(n)) time, which is optimal.
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"abstract": "We investigate the generalisation of quantum search of unstructured and\ntotally ordered sets to search of partially ordered sets (posets). Two models\nfor poset search are considered. In both models, we show that quantum\nalgorithms can achieve at most a quadratic improvement in query complexity over\nclassical algorithms, up to logarithmic factors; we also give quantum\nalgorithms that almost achieve this optimal reduction in complexity. In one\nmodel, we give an improved quantum algorithm for searching forest-like posets;\nin the other, we give an optimal O(sqrt(m))-query quantum algorithm for\nsearching posets derived from m*m arrays sorted by rows and columns. This leads\nto a quantum algorithm that finds the intersection of two sorted lists of n\nintegers in O(sqrt(n)) time, which is optimal.",
"arxiv_id": "quant-ph/0702196",
"authors": [
"Ashley Montanaro"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Information \u0026 Computation, vol. 9, no. 7\u00268, pp. 0628-0647,\n 2009",
"title": "Quantum search of partially ordered sets",
"url": "https://arxiv.org/abs/quant-ph/0702196"
},
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