Unstructured randomness, small gaps and localization
published in arxiv only per Mat Willmott.
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Cornell University Library
2011
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| Online Access: | http://hdl.handle.net/1721.1/64703 https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0003-4626-5648 |
| _version_ | 1826203967168708608 |
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| author | Farhi, Edward Goldstone, Jeffrey Gosset, David Nicholas Gutmann, Sam Shor, Peter W. |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Farhi, Edward Goldstone, Jeffrey Gosset, David Nicholas Gutmann, Sam Shor, Peter W. |
| author_sort | Farhi, Edward |
| collection | MIT |
| description | published in arxiv only per Mat Willmott. |
| first_indexed | 2024-09-23T12:46:44Z |
| format | Article |
| id | mit-1721.1/64703 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:46:44Z |
| publishDate | 2011 |
| publisher | Cornell University Library |
| record_format | dspace |
| spelling | mit-1721.1/647032022-09-28T09:57:01Z Unstructured randomness, small gaps and localization Farhi, Edward Goldstone, Jeffrey Gosset, David Nicholas Gutmann, Sam Shor, Peter W. Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Mathematics Massachusetts Institute of Technology. Department of Physics Farhi, Edward Farhi, Edward Goldstone, Jeffrey Gosset, David Nicholas Shor, Peter W. published in arxiv only per Mat Willmott. We study the Hamiltonian associated with the quantum adiabatic algorithm with a random cost function. Because the cost function lacks structure we can prove results about the ground state. We find the ground state energy as the number of bits goes to infinity, show that the minimum gap goes to zero exponentially quickly, and we see a localization transition. We prove that there are no levels approaching the ground state near the end of the evolution. We do not know which features of this model are shared by a quantum adiabatic algorithm applied to random instances of satisfiability since despite being random they do have bit structure. W. M. Keck Foundation Center for Extreme Quantum Information Theory United States. Army Research Laboratory (ARO grant number W911NF-09-1-0438) National Science Foundation (U.S.) (grant number CCF-0829421) Natural Sciences and Engineering Research Council of Canada 2011-06-29T15:32:10Z 2011-06-29T15:32:10Z 2010-09 Article http://purl.org/eprint/type/JournalArticle arXiv:1010.0009v1 [quant-ph] MIT-CTP/4181 http://hdl.handle.net/1721.1/64703 Farhi, Edward et al. "Unstructured Randomness, Small Gaps and Localization." 30 Sep 2010, arXiv.org, Cornell University Library. https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0003-4626-5648 en_US http://arxiv.org/abs/1010.0009 arXiv.org Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Cornell University Library Prof. Farhi via Mat Willmott |
| spellingShingle | Farhi, Edward Goldstone, Jeffrey Gosset, David Nicholas Gutmann, Sam Shor, Peter W. Unstructured randomness, small gaps and localization |
| title | Unstructured randomness, small gaps and localization |
| title_full | Unstructured randomness, small gaps and localization |
| title_fullStr | Unstructured randomness, small gaps and localization |
| title_full_unstemmed | Unstructured randomness, small gaps and localization |
| title_short | Unstructured randomness, small gaps and localization |
| title_sort | unstructured randomness small gaps and localization |
| url | http://hdl.handle.net/1721.1/64703 https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0003-4626-5648 |
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