{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T16:26:27Z","timestamp":1750436787050,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":27,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642038150"},{"type":"electronic","value":"9783642038167"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-03816-7_56","type":"book-chapter","created":{"date-parts":[[2009,8,19]],"date-time":"2009-08-19T14:43:03Z","timestamp":1250692983000},"page":"663-674","source":"Crossref","is-referenced-by-count":7,"title":["Quantum Algorithms to Solve the Hidden Shift Problem for Quadratics and for Functions of Large Gowers Norm"],"prefix":"10.1007","author":[{"given":"Martin","family":"R\u00f6tteler","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"56_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1007\/978-3-540-45198-3_17","volume-title":"Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques","author":"N. Alon","year":"2003","unstructured":"Alon, N., Kaufman, T., Krivelevich, M., Litsyn, S.N., Ron, D.: Testing low-degree polynomials over GF(2). In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds.) RANDOM 2003 and APPROX 2003. LNCS, vol.\u00a02764, pp. 188\u2013199. Springer, Heidelberg (2003)"},{"issue":"5","key":"56_CR2","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s11128-007-0061-6","volume":"6","author":"A. Atici","year":"2007","unstructured":"Atici, A., Servedio, R.: Quantum algorithms for learning and testing juntas. Quantum Information Processing\u00a06(5), 323\u2013348 (2007)","journal-title":"Quantum Information Processing"},{"key":"56_CR3","doi-asserted-by":"crossref","unstructured":"Bacon, D., Childs, A., van Dam, W.: From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups. In: Proc.\u00a0FOCS 2005, pp. 469\u2013478 (2005)","DOI":"10.1109\/SFCS.2005.38"},{"key":"56_CR4","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1109\/ISTCS.1997.595153","volume-title":"Proceedings of Fifth Israeli Symposium on Theory of Computing and Systems, ISTCS","author":"G. Brassard","year":"1997","unstructured":"Brassard, G., H\u00f8yer, P.: An exact polynomial\u2013time algorithm for Simon\u2019s problem. In: Proceedings of Fifth Israeli Symposium on Theory of Computing and Systems, ISTCS, pp. 12\u201333. IEEE Computer Society Press, Los Alamitos (1997)"},{"issue":"4","key":"56_CR5","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1145\/792538.792543","volume":"50","author":"A. Blum","year":"2003","unstructured":"Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. Journal of the ACM\u00a050(4), 506\u2013519 (2003)","journal-title":"Journal of the ACM"},{"key":"56_CR6","doi-asserted-by":"publisher","first-page":"167902","DOI":"10.1103\/PhysRevLett.87.167902","volume":"87","author":"H. Buhrman","year":"2001","unstructured":"Buhrman, H., Cleve, R., Watrous, J., de Wolf, R.: Quantum fingerprinting. Phys. Rev. Letters\u00a087, 167902 (4 pages) (2001)","journal-title":"Phys. Rev. Letters"},{"issue":"5","key":"56_CR7","doi-asserted-by":"publisher","first-page":"1411","DOI":"10.1137\/S0097539796300921","volume":"26","author":"E. Bernstein","year":"1997","unstructured":"Bernstein, E., Vazirani, U.: Quantum complexity theory. SIAM Journal on Computing\u00a026(5), 1411\u20131473 (1997); Conference version in Proc. STOC 1993, pp.\u00a011\u201320 (1993)","journal-title":"SIAM Journal on Computing"},{"key":"56_CR8","doi-asserted-by":"crossref","unstructured":"Childs, A., Schulman, L.J., Vazirani, U.: Quantum algorithms for hidden nonlinear structures. In: Proc.\u00a0FOCS 2007, pp. 395\u2013404 (2007)","DOI":"10.1109\/FOCS.2007.18"},{"key":"56_CR9","doi-asserted-by":"crossref","first-page":"215","DOI":"10.26421\/QIC9.3-4-3","volume":"9","author":"T. Decker","year":"2009","unstructured":"Decker, T., Draisma, J., Wocjan, P.: Efficient quantum algorithm for identifying hidden polynomials. Quantum Information and Computation\u00a09, 215\u2013230 (2009)","journal-title":"Quantum Information and Computation"},{"key":"56_CR10","unstructured":"van Dam, W., Hallgren, S., Ip, L.: Quantum algorithms for some hidden shift problems. In: Proc.\u00a0SODA 2003, pp. 489\u2013498 (2003)"},{"key":"56_CR11","unstructured":"Dillon, J.: Elementary Hadamard difference sets. In: Hoffman, F., et al. (eds.) Proc. 6th S-E Conf. on Combinatorics, Graph Theory, and Computing, pp. 237\u2013249. Winnipeg Utilitas Math. (1975)"},{"key":"56_CR12","doi-asserted-by":"crossref","unstructured":"Friedl, K., Ivanyos, G., Magniez, F., Santha, M., Sen, P.: Hidden translation and orbit coset in quantum computing. In: Proc.\u00a0STOC 2003, pp. 1\u20139 (2003)","DOI":"10.1145\/780542.780544"},{"key":"56_CR13","unstructured":"Green, B., Tao, T.: An inverse theorem for the Gowers U 3(G) norm. Proc. Edin. Math. Soc. (2008); see also arxiv preprint math.NT\/0503014 (to appear)"},{"key":"56_CR14","doi-asserted-by":"crossref","unstructured":"Hallgren, S., Moore, C., R\u00f6tteler, M., Russell, A., Sen, P.: Limitations of quantum coset states for graph isomorphism. In: Proc.\u00a0STOC 2006, pp. 604\u2013617 (2006)","DOI":"10.1145\/1132516.1132603"},{"issue":"6","key":"56_CR15","doi-asserted-by":"publisher","first-page":"1191","DOI":"10.1070\/RM1997v052n06ABEH002155","volume":"52","author":"A. Yu","year":"1997","unstructured":"Yu, A.: Kitaev. Quantum computations: algorithms and error correction. Russian Math. Surveys\u00a052(6), 1191\u20131249 (1997)","journal-title":"Russian Math. Surveys"},{"issue":"1","key":"56_CR16","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1137\/S0097539703436345","volume":"35","author":"G. Kuperberg","year":"2005","unstructured":"Kuperberg, G.: A subexponential-time quantum algorithm for the dihedral hidden subgroup problem. SIAM Journal on Computing\u00a035(1), 170\u2013188 (2005)","journal-title":"SIAM Journal on Computing"},{"key":"56_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1007\/3-540-49208-9_15","volume-title":"Quantum Computing and Quantum Communications","author":"M. Mosca","year":"1999","unstructured":"Mosca, M., Ekert, A.: The hidden subgroup problem and eigenvalue estimation on a quantum computer. In: Williams, C.P. (ed.) QCQC 1998. LNCS, vol.\u00a01509, pp. 174\u2013188. Springer, Heidelberg (1999)"},{"issue":"5&6","key":"56_CR18","doi-asserted-by":"crossref","first-page":"500","DOI":"10.26421\/QIC9.5-6-10","volume":"9","author":"A. Montanaro","year":"2009","unstructured":"Montanaro, A.: Quantum algorithms for shifted subset problems. Quantum Information and Computation\u00a09(5&6), 500\u2013512 (2009)","journal-title":"Quantum Information and Computation"},{"key":"56_CR19","volume-title":"The Theory of Error\u2013Correcting Codes","author":"F.J. MacWilliams","year":"1977","unstructured":"MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error\u2013Correcting Codes. North\u2013Holland, Amsterdam (1977)"},{"key":"56_CR20","volume-title":"Quantum Computation and Quantum Information","author":"M. Nielsen","year":"2000","unstructured":"Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)"},{"key":"56_CR21","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1016\/0097-3165(76)90024-8","volume":"20","author":"O.S. Rothaus","year":"1976","unstructured":"Rothaus, O.S.: On \u201cbent\u201d functions. Journal of Combinatorial Theory, Series A\u00a020, 300\u2013305 (1976)","journal-title":"Journal of Combinatorial Theory, Series A"},{"key":"56_CR22","unstructured":"R\u00f6tteler, M.: Quantum algorithms for highly non-linear boolean functions. arXiv Preprint 0811.3208 (2008)"},{"issue":"2-3","key":"56_CR23","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1016\/j.jco.2003.08.019","volume":"20","author":"A. Russell","year":"2004","unstructured":"Russell, A., Shparlinski, I.: Classical and quantum function reconstruction via character evaluation. Journal of Complexity\u00a020(2-3), 404\u2013422 (2004)","journal-title":"Journal of Complexity"},{"key":"56_CR24","doi-asserted-by":"crossref","unstructured":"Samorodnitsky, A.: Low-degree tests at large distances. In: Proceedings of the 39th Annual ACM Symposium on Theory of Computing (STOC 2007), pp. 506\u2013515 (2007)","DOI":"10.1145\/1250790.1250864"},{"issue":"5","key":"56_CR25","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1137\/S0097539795293172","volume":"26","author":"P. Shor","year":"1997","unstructured":"Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing\u00a026(5), 1484\u20131509 (1997)","journal-title":"SIAM Journal on Computing"},{"key":"56_CR26","doi-asserted-by":"crossref","unstructured":"Samorodnitsky, A., Trevisan, T.: Gowers uniformity, influence of variables, and PCPs. In: Proc.\u00a0STOC 2006, pp. 11\u201320 (2006)","DOI":"10.1145\/1132516.1132519"},{"key":"56_CR27","doi-asserted-by":"crossref","unstructured":"Watrous, J.: Succinct quantum proofs for properties of finite groups. In: Proc.\u00a0FOCS 2000, pp. 537\u2013546 (2000)","DOI":"10.1109\/SFCS.2000.892141"}],"container-title":["Lecture Notes in Computer Science","Mathematical Foundations of Computer Science 2009"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-03816-7_56","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T19:57:29Z","timestamp":1739303849000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-03816-7_56"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642038150","9783642038167"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-03816-7_56","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2009]]}}}