dorsal/arxiv
View SchemaExponential algorithmic speedup by quantum walk
| Authors | Andrew M. Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann, Daniel A. Spielman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209131 |
| URL | https://arxiv.org/abs/quant-ph/0209131 |
| DOI | 10.1145/780542.780552 |
| Journal | Proc. 35th ACM Symposium on Theory of Computing (STOC 2003), pp. 59-68 |
Abstract
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our oracular setting. We then show how this quantum walk can be used to solve our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve this problem with high probability in subexponential time.
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"abstract": "We construct an oracular (i.e., black box) problem that can be solved\nexponentially faster on a quantum computer than on a classical computer. The\nquantum algorithm is based on a continuous time quantum walk, and thus employs\na different technique from previous quantum algorithms based on quantum Fourier\ntransforms. We show how to implement the quantum walk efficiently in our\noracular setting. We then show how this quantum walk can be used to solve our\nproblem by rapidly traversing a graph. Finally, we prove that no classical\nalgorithm can solve this problem with high probability in subexponential time.",
"arxiv_id": "quant-ph/0209131",
"authors": [
"Andrew M. Childs",
"Richard Cleve",
"Enrico Deotto",
"Edward Farhi",
"Sam Gutmann",
"Daniel A. Spielman"
],
"categories": [
"quant-ph"
],
"doi": "10.1145/780542.780552",
"journal_ref": "Proc. 35th ACM Symposium on Theory of Computing (STOC 2003), pp.\n 59-68",
"title": "Exponential algorithmic speedup by quantum walk",
"url": "https://arxiv.org/abs/quant-ph/0209131"
},
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