{"doi":"10.1137/110842272","page":"1028-1050","publication_status":"published","issue":"4","date_created":"2019-03-01T12:04:03Z","abstract":[{"text":"Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem (where QMA stands for Quantum Merlin Arthur) and initiate its study. We present two main results. The first shows that a nontrivial approximation ratio can be obtained in the class NP using product states. The second result (which builds on the first one) gives a polynomial time (classical) algorithm providing a similar approximation ratio for dense instances of the problem. The latter result is based on an adaptation of the “exhaustive sampling method” by Arora, Karger, and Karpinski [J. Comput. System Sci., 58 (1999), p. 193] to the quantum setting and might be of independent interest.","lang":"eng"}],"oa":"1","article_type":"original","type":"journal_article","date_updated":"2023-02-28T11:03:50Z","publication":"SIAM Journal on Computing","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1101.3884"}],"_id":"8175","title":"Approximation Algorithms for QMA-Complete Problems","department":[{"_id":"623"},{"_id":"7"}],"publication_identifier":{"issn":["0097-5397","1095-7111"]},"volume":41,"user_id":"71541","external_id":{"arxiv":["1101.3884"]},"citation":{"chicago":"Gharibian, Sevag, and Julia Kempe. “Approximation Algorithms for QMA-Complete Problems.” <i>SIAM Journal on Computing</i> 41, no. 4 (2012): 1028–50. <a href=\"https://doi.org/10.1137/110842272\">https://doi.org/10.1137/110842272</a>.","short":"S. Gharibian, J. Kempe, SIAM Journal on Computing 41 (2012) 1028–1050.","bibtex":"@article{Gharibian_Kempe_2012, title={Approximation Algorithms for QMA-Complete Problems}, volume={41}, DOI={<a href=\"https://doi.org/10.1137/110842272\">10.1137/110842272</a>}, number={4}, journal={SIAM Journal on Computing}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Gharibian, Sevag and Kempe, Julia}, year={2012}, pages={1028–1050} }","apa":"Gharibian, S., &#38; Kempe, J. (2012). Approximation Algorithms for QMA-Complete Problems. <i>SIAM Journal on Computing</i>, <i>41</i>(4), 1028–1050. <a href=\"https://doi.org/10.1137/110842272\">https://doi.org/10.1137/110842272</a>","ieee":"S. Gharibian and J. Kempe, “Approximation Algorithms for QMA-Complete Problems,” <i>SIAM Journal on Computing</i>, vol. 41, no. 4, pp. 1028–1050, 2012, doi: <a href=\"https://doi.org/10.1137/110842272\">10.1137/110842272</a>.","ama":"Gharibian S, Kempe J. Approximation Algorithms for QMA-Complete Problems. <i>SIAM Journal on Computing</i>. 2012;41(4):1028-1050. doi:<a href=\"https://doi.org/10.1137/110842272\">10.1137/110842272</a>","mla":"Gharibian, Sevag, and Julia Kempe. “Approximation Algorithms for QMA-Complete Problems.” <i>SIAM Journal on Computing</i>, vol. 41, no. 4, Society for Industrial &#38; Applied Mathematics (SIAM), 2012, pp. 1028–50, doi:<a href=\"https://doi.org/10.1137/110842272\">10.1137/110842272</a>."},"status":"public","intvolume":"        41","year":"2012","extern":"1","publisher":"Society for Industrial & Applied Mathematics (SIAM)","author":[{"orcid":"0000-0002-9992-3379","first_name":"Sevag","id":"71541","last_name":"Gharibian","full_name":"Gharibian, Sevag"},{"full_name":"Kempe, Julia","last_name":"Kempe","first_name":"Julia"}]}