[{"publication_identifier":{"unknown":["978-3-95977-086-6"]},"author":[{"full_name":"Gharibian, Sevag","last_name":"Gharibian","first_name":"Sevag","orcid":"0000-0002-9992-3379","id":"71541"},{"first_name":"Miklos","last_name":"Santha","full_name":"Santha, Miklos"},{"full_name":"Sikora, Jamie","last_name":"Sikora","first_name":"Jamie"},{"last_name":"Sundaram","first_name":"Aarthi","full_name":"Sundaram, Aarthi"},{"last_name":"Yirka","first_name":"Justin","full_name":"Yirka, Justin"}],"title":"Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2)","year":"2018","intvolume":"       117","publication_status":"published","date_updated":"2023-02-28T11:01:03Z","language":[{"iso":"eng"}],"series_title":"Leibniz International Proceedings in Informatics (LIPIcs)","main_file_link":[{"url":"http://drops.dagstuhl.de/opus/frontdoor.php?source_opus=9640","open_access":"1"}],"doi":"10.4230/LIPIcs.MFCS.2018.58","publication":"43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)","abstract":[{"lang":"eng","text":"The polynomial-time hierarchy (PH) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as PH does not collapse). Here, we study whether two quantum generalizations of PH can similarly prove separations in the quantum setting. The first generalization, QCPH, uses classical proofs, and the second, QPH, uses quantum proofs. For the former, we show quantum variants of the Karp-Lipton theorem and Toda's theorem. For the latter, we place its third level, Q Sigma_3, into NEXP using the Ellipsoid Method for efficiently solving semidefinite programs. These results yield two implications for QMA(2), the variant of Quantum Merlin-Arthur (QMA) with two unentangled proofs, a complexity class whose characterization has proven difficult. First, if QCPH=QPH (i.e., alternating quantifiers are sufficiently powerful so as to make classical and quantum proofs \"equivalent\"), then QMA(2) is in the Counting Hierarchy (specifically, in P^{PP^{PP}}). Second, unless QMA(2)= Q Sigma_3 (i.e., alternating quantifiers do not help in the presence of \"unentanglement\"), QMA(2) is strictly contained in NEXP."}],"date_created":"2019-03-01T11:29:44Z","department":[{"_id":"623"},{"_id":"7"}],"type":"conference","keyword":["Complexity Theory","Quantum Computing","Polynomial Hierarchy","Semidefinite Programming","QMA(2)","Quantum Complexity"],"conference":{"name":"43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)","location":"Liverpool, UK"},"status":"public","publisher":"Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik","_id":"8161","page":"58:1-58:16","volume":117,"editor":[{"full_name":"Potapov, Igor","first_name":"Igor","last_name":"Potapov"},{"last_name":"Spirakis","first_name":"Paul","full_name":"Spirakis, Paul"},{"last_name":"Worrell","first_name":"James","full_name":"Worrell, James"}],"user_id":"71541","citation":{"mla":"Gharibian, Sevag, et al. “Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2).” <i>43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)</i>, edited by Igor Potapov et al., vol. 117, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018, p. 58:1-58:16, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2018.58\">10.4230/LIPIcs.MFCS.2018.58</a>.","ama":"Gharibian S, Santha M, Sikora J, Sundaram A, Yirka J. Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2). In: Potapov I, Spirakis P, Worrell J, eds. <i>43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)</i>. Vol 117. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik; 2018:58:1-58:16. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2018.58\">10.4230/LIPIcs.MFCS.2018.58</a>","bibtex":"@inproceedings{Gharibian_Santha_Sikora_Sundaram_Yirka_2018, place={Dagstuhl, Germany}, series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2)}, volume={117}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2018.58\">10.4230/LIPIcs.MFCS.2018.58</a>}, booktitle={43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)}, publisher={Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik}, author={Gharibian, Sevag and Santha, Miklos and Sikora, Jamie and Sundaram, Aarthi and Yirka, Justin}, editor={Potapov, Igor and Spirakis, Paul and Worrell, James}, year={2018}, pages={58:1-58:16}, collection={Leibniz International Proceedings in Informatics (LIPIcs)} }","apa":"Gharibian, S., Santha, M., Sikora, J., Sundaram, A., &#38; Yirka, J. (2018). Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2). In I. Potapov, P. Spirakis, &#38; J. Worrell (Eds.), <i>43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)</i> (Vol. 117, p. 58:1-58:16). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2018.58\">https://doi.org/10.4230/LIPIcs.MFCS.2018.58</a>","ieee":"S. Gharibian, M. Santha, J. Sikora, A. Sundaram, and J. Yirka, “Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2),” in <i>43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)</i>, Liverpool, UK, 2018, vol. 117, p. 58:1-58:16, doi: <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2018.58\">10.4230/LIPIcs.MFCS.2018.58</a>.","short":"S. Gharibian, M. Santha, J. Sikora, A. Sundaram, J. Yirka, in: I. Potapov, P. Spirakis, J. Worrell (Eds.), 43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018), Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2018, p. 58:1-58:16.","chicago":"Gharibian, Sevag, Miklos Santha, Jamie Sikora, Aarthi Sundaram, and Justin Yirka. “Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2).” In <i>43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)</i>, edited by Igor Potapov, Paul Spirakis, and James Worrell, 117:58:1-58:16. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2018.58\">https://doi.org/10.4230/LIPIcs.MFCS.2018.58</a>."},"place":"Dagstuhl, Germany","external_id":{"arxiv":["1805.11139"]},"oa":"1"},{"citation":{"mla":"Douglas, Pamela Heidi, et al. “A Novel Approach for Dominance Assessment in Gregarious Species: ADAGIO.” <i>Animal Behaviour</i>, vol. 123, Elsevier BV, 2016, pp. 21–32, doi:<a href=\"https://doi.org/10.1016/j.anbehav.2016.10.014\">10.1016/j.anbehav.2016.10.014</a>.","ama":"Douglas PH, Ngonga Ngomo A-C, Hohmann G. A novel approach for dominance assessment in gregarious species: ADAGIO. <i>Animal Behaviour</i>. 2016;123:21-32. doi:<a href=\"https://doi.org/10.1016/j.anbehav.2016.10.014\">10.1016/j.anbehav.2016.10.014</a>","bibtex":"@article{Douglas_Ngonga Ngomo_Hohmann_2016, title={A novel approach for dominance assessment in gregarious species: ADAGIO}, volume={123}, DOI={<a href=\"https://doi.org/10.1016/j.anbehav.2016.10.014\">10.1016/j.anbehav.2016.10.014</a>}, journal={Animal Behaviour}, publisher={Elsevier BV}, author={Douglas, Pamela Heidi and Ngonga Ngomo, Axel-Cyrille and Hohmann, Gottfried}, year={2016}, pages={21–32} }","apa":"Douglas, P. H., Ngonga Ngomo, A.-C., &#38; Hohmann, G. (2016). A novel approach for dominance assessment in gregarious species: ADAGIO. <i>Animal Behaviour</i>, <i>123</i>, 21–32. <a href=\"https://doi.org/10.1016/j.anbehav.2016.10.014\">https://doi.org/10.1016/j.anbehav.2016.10.014</a>","ieee":"P. H. Douglas, A.-C. Ngonga Ngomo, and G. Hohmann, “A novel approach for dominance assessment in gregarious species: ADAGIO,” <i>Animal Behaviour</i>, vol. 123, pp. 21–32, 2016, doi: <a href=\"https://doi.org/10.1016/j.anbehav.2016.10.014\">10.1016/j.anbehav.2016.10.014</a>.","chicago":"Douglas, Pamela Heidi, Axel-Cyrille Ngonga Ngomo, and Gottfried Hohmann. “A Novel Approach for Dominance Assessment in Gregarious Species: ADAGIO.” <i>Animal Behaviour</i> 123 (2016): 21–32. <a href=\"https://doi.org/10.1016/j.anbehav.2016.10.014\">https://doi.org/10.1016/j.anbehav.2016.10.014</a>.","short":"P.H. Douglas, A.-C. Ngonga Ngomo, G. Hohmann, Animal Behaviour 123 (2016) 21–32."},"status":"public","volume":123,"user_id":"72311","publisher":"Elsevier BV","_id":"61025","page":"21-32","abstract":[{"lang":"eng","text":"The concept of social dominance has been used in a plethora of studies to assess animal behaviour and relationships between individuals for nearly a century. Nevertheless, a standard approach does not yet exist to assess dominance in species that have a nonlinear or weakly linear hierarchical structure. We amassed 316 published data sets and show that 73.7% of the data sets and 90.3% of 103 species that we reviewed do not have a strongly linear structure. Herein, we present a novel method, ADAGIO, for assessing the structure of dominance networks. ADAGIO computes dominance hierarchies, in the form of directed acyclic graphs, to represent the dominance relations of a given group of animals. Thus far, most methods for computing dominance ranks assume implicitly that the dominance relation is a total order of the individuals in a group. ADAGIO does not assume or require this to be always true, and is hence more appropriate for analysing dominance hierarchies that are not strongly linear. We evaluated our approach against other frequently used methods, I&SI, David's score and Elo-rating, on 12 000 simulated data sets and on 279 interaction matrices from published, empirical data. The results from the simulated data show that ADAGIO achieves a significantly smaller error, and hence performs better when assigning ranks than other methods. Additionally, ADAGIO generated accurate dominance hierarchies for empirical data sets with a high index of linearity. Hence, our findings suggest that ADAGIO is currently the most reliable method to assess social dominance in gregarious animals living in groups of any size. Furthermore, since ADAGIO was designed to be generic, its applicability has the potential to extend beyond dominance data. The source code of our algorithm and all simulations used for this paper are publicly available at http://ngonga.github.io/adagio/."}],"extern":"1","publication":"Animal Behaviour","department":[{"_id":"40"}],"type":"journal_article","keyword":["aggression","behaviour","comparability","directed acyclic graph","hierarchy","linearity","nonlinearity","social rank","totality"],"date_created":"2025-08-26T19:24:18Z","intvolume":"       123","article_type":"original","date_updated":"2025-08-26T19:57:38Z","publication_status":"published","publication_identifier":{"issn":["0003-3472"]},"author":[{"id":"72311","full_name":"Douglas, Pamela Heidi","last_name":"Douglas","first_name":"Pamela Heidi"},{"id":"65716","full_name":"Ngonga Ngomo, Axel-Cyrille","first_name":"Axel-Cyrille","last_name":"Ngonga Ngomo"},{"last_name":"Hohmann","first_name":"Gottfried","full_name":"Hohmann, Gottfried"}],"year":"2016","title":"A novel approach for dominance assessment in gregarious species: ADAGIO","doi":"10.1016/j.anbehav.2016.10.014","language":[{"iso":"eng"}]},{"status":"public","volume":14,"user_id":"71541","_id":"8171","page":"517-540","citation":{"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.","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.","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} }","ama":"Gharibian S, Kempe J. Hardness of approximation for quantum problems. <i>Quantum Information &#38; Computation</i>. 2014;14(5-6):517-540."},"oa":"1","external_id":{"arxiv":["1209.1055"]},"intvolume":"        14","article_type":"original","date_updated":"2023-02-28T11:02:47Z","publication_status":"published","author":[{"orcid":"0000-0002-9992-3379","first_name":"Sevag","last_name":"Gharibian","full_name":"Gharibian, Sevag","id":"71541"},{"full_name":"Kempe, Julia","last_name":"Kempe","first_name":"Julia"}],"year":"2014","title":"Hardness of approximation for quantum problems","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1209.1055","open_access":"1"}],"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."}],"extern":"1","issue":"5-6","publication":"Quantum Information & Computation","department":[{"_id":"623"},{"_id":"7"}],"type":"journal_article","keyword":["Hardness of approximation","polynomial time hierarchy","succinct set cover","quantum complexity"],"date_created":"2019-03-01T11:56:55Z"}]