dorsal/arxiv
View SchemaQuantum Computation and Decision Trees
| Authors | Edward Farhi, Sam Gutmann |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9706062 |
| URL | https://arxiv.org/abs/quant-ph/9706062 |
| DOI | 10.1103/PhysRevA.58.915 |
Abstract
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root. We devise a quantum mechanical algorithm that evolves a state, initially localized at the root, through the tree. We prove that if the classical strategy succeeds in reaching level n in time polynomial in n, then so does the quantum algorithm. Moreover, we find examples of trees for which the classical algorithm requires time exponential in n, but for which the quantum algorithm succeeds in polynomial time. The examples we have so far, however, could also be solved in polynomial time by different classical algorithms.
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"abstract": "Many interesting computational problems can be reformulated in terms of\ndecision trees. A natural classical algorithm is to then run a random walk on\nthe tree, starting at the root, to see if the tree contains a node n levels\nfrom the root. We devise a quantum mechanical algorithm that evolves a state,\ninitially localized at the root, through the tree. We prove that if the\nclassical strategy succeeds in reaching level n in time polynomial in n, then\nso does the quantum algorithm. Moreover, we find examples of trees for which\nthe classical algorithm requires time exponential in n, but for which the\nquantum algorithm succeeds in polynomial time. The examples we have so far,\nhowever, could also be solved in polynomial time by different classical\nalgorithms.",
"arxiv_id": "quant-ph/9706062",
"authors": [
"Edward Farhi",
"Sam Gutmann"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.58.915",
"title": "Quantum Computation and Decision Trees",
"url": "https://arxiv.org/abs/quant-ph/9706062"
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