{"publication_status":"published","date_updated":"2023-02-28T11:02:47Z","extern":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["1209.1055"]},"title":"Hardness of approximation for quantum problems","department":[{"_id":"623"},{"_id":"7"}],"citation":{"mla":"Gharibian, Sevag, and Julia Kempe. “Hardness of Approximation for Quantum Problems.” <i>Quantum Information &#38; Computation</i>, vol. 14, no. 5–6, 2014, pp. 517–40.","ieee":"S. Gharibian and J. Kempe, “Hardness of approximation for quantum problems,” <i>Quantum Information &#38; Computation</i>, vol. 14, no. 5–6, pp. 517–540, 2014.","apa":"Gharibian, S., &#38; Kempe, J. (2014). Hardness of approximation for quantum problems. <i>Quantum Information &#38; Computation</i>, <i>14</i>(5–6), 517–540.","short":"S. Gharibian, J. Kempe, Quantum Information &#38; Computation 14 (2014) 517–540.","chicago":"Gharibian, Sevag, and Julia Kempe. “Hardness of Approximation for Quantum Problems.” <i>Quantum Information &#38; Computation</i> 14, no. 5–6 (2014): 517–40.","ama":"Gharibian S, Kempe J. Hardness of approximation for quantum problems. <i>Quantum Information &#38; Computation</i>. 2014;14(5-6):517-540.","bibtex":"@article{Gharibian_Kempe_2014, title={Hardness of approximation for quantum problems}, volume={14}, number={5–6}, journal={Quantum Information &#38; Computation}, author={Gharibian, Sevag and Kempe, Julia}, year={2014}, pages={517–540} }"},"user_id":"71541","article_type":"original","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1209.1055"}],"status":"public","author":[{"first_name":"Sevag","orcid":"0000-0002-9992-3379","id":"71541","last_name":"Gharibian","full_name":"Gharibian, Sevag"},{"first_name":"Julia","last_name":"Kempe","full_name":"Kempe, Julia"}],"intvolume":"        14","_id":"8171","year":"2014","type":"journal_article","page":"517-540","publication":"Quantum Information & Computation","issue":"5-6","date_created":"2019-03-01T11:56:55Z","keyword":["Hardness of approximation","polynomial time hierarchy","succinct set cover","quantum complexity"],"oa":"1","volume":14,"abstract":[{"lang":"eng","text":"The polynomial hierarchy plays a central role in classical complexity theory. Here, we define\r\na quantum generalization of the polynomial hierarchy, and initiate its study. We show that\r\nnot only are there natural complete problems for the second level of this quantum hierarchy, but that these problems are in fact hard to approximate. Using the same techniques, we\r\nalso obtain hardness of approximation for the class QCMA. Our approach is based on the\r\nuse of dispersers, and is inspired by the classical results of Umans regarding hardness of approximation for the second level of the classical polynomial hierarchy [Umans, FOCS 1999].\r\nThe problems for which we prove hardness of approximation for include, among others, a\r\nquantum version of the Succinct Set Cover problem, and a variant of the local Hamiltonian\r\nproblem with hybrid classical-quantum ground states."}]}