{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,25]],"date-time":"2026-10-25T17:51:43Z","timestamp":1792950703318,"version":"4.5.0"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube $\\left\\{0,1\\right\\}^n$, we show a lower bound of $\\Omega\\left(2^{n\/4}\/n\\right)$ on the number of queries needed by a quantum computer to solve this problem. More surprisingly, our approach, based on Ambainis's quantum adversary method, also yields a lower bound of $\\Omega\\left(2^{n\/2}\/n^2\\right)$ on the problem's classical randomized query complexity. This improves and simplifies a 1983 result of Aldous. Finally, in both the randomized and quantum cases, we give the first nontrivial lower bounds for finding local minima on grids of constant dimension $d\\geq3$.<\/jats:p>","DOI":"10.1137\/s0097539704447237","type":"journal-article","created":{"date-parts":[[2006,3,14]],"date-time":"2006-03-14T18:03:10Z","timestamp":1142359390000},"page":"804-824","source":"Crossref","is-referenced-by-count":28,"title":["Lower Bounds for Local Search by Quantum Arguments"],"prefix":"10.1137","volume":"35","author":[{"given":"Scott","family":"Aaronson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,27]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Scott Aaronson, Quantum lower bound for the collision problem, ACM, New York, 2002, 635\u20136422121190","DOI":"10.1145\/509907.509999"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"D. Aharonov and O. Regev,\n                      Lattice problems in NP intersect coNP\n                      , in Proceedings of IEEE FOCS, 2004, pp. 362\u2013371.","DOI":"10.1109\/FOCS.2004.35"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993605"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.2002.1826"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"A. Ambainis,\n                      Polynomial degree vs. quantum query complexity\n                      , in Proceedings of IEEE FOCS, 2003, pp. 230\u2013239 (quant\u2010ph\/0305028).","DOI":"10.1109\/SFCS.2003.1238197"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0204037"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1145\/502090.502097"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539796300933"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(01)00144-X"},{"key":"R10","volume-title":"Graph theory","author":"Diestel Reinhard","year":"2000"},{"key":"R11","unstructured":"S. Droste, T. Jansen, and I. Wegener,\n                      Upper and lower bounds for randomized search heuristics in black\u2010box optimization\n                      , Theory Comput. Syst., to appear."},{"key":"R12","unstructured":"C. D\u00fcrr and P. H\u00f8yer,\n                      A quantum algorithm for finding the minimum\n                      , 1996 (quant\u2010ph\/9607014)."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1126\/science.1057726"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(88)90046-3"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"Iordanis Kerenidis, Ronald de Wolf, Exponential lower bound for 2\u2010query locally decodable codes via a quantum argument, ACM, New York, 2003, 106\u20131152005k:94037","DOI":"10.1145\/780542.780560"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"S. Laplante and F. Magniez,\n                      Lower bounds for randomized and quantum query complexity using Kolmogorov arguments\n                      , in Proceedings of IEEE Conference on Computational Complexity, 2004, pp. 294\u2013304 (quant\u2010ph\/0311189).","DOI":"10.1109\/CCC.2004.1313852"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(93)90004-8"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(89)90025-5"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(93)90161-G"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(91)90200-L"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814075"},{"key":"R22","unstructured":"C. H. Papadimitriou, talk at UC Berkeley, February 6, 2003."},{"key":"R23","doi-asserted-by":"crossref","unstructured":"Miklos Santha, Mario Szegedy, Quantum and classical query complexities of local search are polynomially related, ACM, New York, 2004, 494\u20135012005j:68031","DOI":"10.1145\/1007352.1007427"},{"key":"R24","unstructured":"Y. Shi,\n                      Quantum lower bounds for the collision and the element distinctness problems\n                      , in Proceedings of IEEE FOCS, 2002, pp. 513\u2013519. quant\u2010ph\/0112086."},{"key":"R25","unstructured":"Y. Verhoeven,\n                      Enhanced algorithms for local search\n                      , Inform. Process. Lett., to appear (quant\u2010ph\/0506019)."},{"key":"R26","doi-asserted-by":"crossref","unstructured":"Robert \u0160palek, Mario Szegedy, All quantum adversary methods are equivalent, Lecture Notes in Comput. Sci., Vol. 3580, Springer, Berlin, 2005, 1299\u201313112184720","DOI":"10.1007\/11523468_105"},{"key":"R27","unstructured":"S. Zhang,\n                      (Almost) tight bounds for randomized and quantum local search on hypercubes and grids\n                      , 2005 (quant\u2010ph\/0504085)."}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539704447237","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:16:55Z","timestamp":1787336215000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539704447237"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/S0097539704447237"],"URL":"https:\/\/doi.org\/10.1137\/s0097539704447237","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}