{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T20:43:56Z","timestamp":1774385036855,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":41,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540899938","type":"print"},{"value":"9783540899945","type":"electronic"}],"license":[{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"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":[[2008]]},"DOI":"10.1007\/978-3-540-89994-5_7","type":"book-chapter","created":{"date-parts":[[2008,12,8]],"date-time":"2008-12-08T05:41:38Z","timestamp":1228714898000},"page":"70-88","source":"Crossref","is-referenced-by-count":7,"title":["An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups"],"prefix":"10.1007","author":[{"given":"Hari","family":"Krovi","sequence":"first","affiliation":[]},{"given":"Martin","family":"R\u00f6tteler","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"#cr-split#-7_CR1.1","doi-asserted-by":"crossref","unstructured":"Ambainis, A., Emerson, J.: Quantum t-designs: t-wise independence in the quantum world. In: Proceedings of the 22nd Annual IEEE Conference on Computational Complexity, pp. 129???140 (2007);","DOI":"10.1109\/CCC.2007.26"},{"key":"#cr-split#-7_CR1.2","unstructured":"Also arxiv preprint quant-ph\/0701126"},{"issue":"5","key":"7_CR2","doi-asserted-by":"crossref","first-page":"438","DOI":"10.26421\/QIC8.5-6","volume":"8","author":"D. Bacon","year":"2008","unstructured":"Bacon, D.: How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem. Quantum Information and Computation\u00a08(5), 438\u2013467 (2008)","journal-title":"Quantum Information and Computation"},{"key":"#cr-split#-7_CR3.1","unstructured":"Bacon, D.: Simon???s algorithm, Clebsch-Gordan sieves, and hidden symmetries of multiple squares (2008);"},{"key":"#cr-split#-7_CR3.2","unstructured":"Arxiv preprint quant-ph\/0808.0174"},{"key":"#cr-split#-7_CR4.1","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: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 469???478 (2005);","DOI":"10.1109\/SFCS.2005.38"},{"key":"#cr-split#-7_CR4.2","unstructured":"Also arxiv preprint quant-ph\/0504083"},{"key":"7_CR5","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1016\/0304-3975(87)90041-7","volume":"51","author":"T.. Beth","year":"1987","unstructured":"Beth, T.: On the computational complexity of the general discrete Fourier transform. Theoretical Computer Science\u00a051, 331\u2013339 (1987)","journal-title":"Theoretical Computer Science"},{"key":"7_CR6","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); Also arxiv preprint quant\u2013ph\/9704027"},{"issue":"3","key":"7_CR7","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1103\/PhysRevLett.78.405","volume":"78","author":"A.R. Calderbank","year":"1997","unstructured":"Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction and orthogonal geometry. Physical Review Letters\u00a078(3), 405\u2013408 (1997); Also arxiv preprint quant-ph\/9605005","journal-title":"Physical Review Letters"},{"issue":"4","key":"7_CR8","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1109\/18.681315","volume":"44","author":"A.R. Calderbank","year":"1998","unstructured":"Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Transactions on Information Theory\u00a044(4), 1369\u20131387 (1998); Also arxiv preprint quant-ph\/9608006","journal-title":"IEEE Transactions on Information Theory"},{"key":"#cr-split#-7_CR9.1","doi-asserted-by":"crossref","unstructured":"Childs, A., Schulman, L.J., Vazirani, U.: Quantum algorithms for hidden nonlinear structures. In: Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, pp. 395???404 (2007);","DOI":"10.1109\/FOCS.2007.18"},{"key":"#cr-split#-7_CR9.2","unstructured":"Also preprint arxiv:0705.2784"},{"key":"#cr-split#-7_CR10.1","unstructured":"van Dam, W., Hallgren, S., Ip, L.: Quantum algorithms for some hidden shift problems. In: Proceedings of the Symposium on Discrete Algorithms (SODA), pp. 489???498 (2003);"},{"key":"#cr-split#-7_CR10.2","unstructured":"Also arxiv preprint quant???ph\/0211140"},{"issue":"1","key":"7_CR11","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.ipl.2004.01.024","volume":"91","author":"M. Ettinger","year":"2004","unstructured":"Ettinger, M., H\u00f8yer, P., Knill, E.: The quantum query complexity of the hidden subgroup problem is polynomial. Information Processing Letters\u00a091(1), 43\u201348 (2004); Also arxiv preprint quant\u2013ph\/0401083","journal-title":"Information Processing Letters"},{"key":"#cr-split#-7_CR12.1","doi-asserted-by":"crossref","unstructured":"Friedl, K., Ivanyos, G., Magniez, F., Santha, M., Sen, P.: Hidden translation and orbit coset in quantum computing. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, pp. 1???9 (2003);","DOI":"10.1145\/780542.780544"},{"key":"#cr-split#-7_CR12.2","unstructured":"Also arxiv preprint quant???ph\/0211091"},{"issue":"3","key":"7_CR13","doi-asserted-by":"publisher","first-page":"1862","DOI":"10.1103\/PhysRevA.54.1862","volume":"54","author":"D. Gottesman","year":"1996","unstructured":"Gottesman, D.: A class of quantum error-correcting codes saturating the quantum Hamming bound. Physical Review A\u00a054(3), 1862\u20131868 (1996); Also arxiv preprint quant-ph\/9604038","journal-title":"Physical Review A"},{"key":"7_CR14","doi-asserted-by":"crossref","unstructured":"Grigni, M., Schulman, L., Vazirani, M., Vazirani, U.: Quantum mechanical algorithms for the nonabelian hidden subgroup problem. Combinatorica, 137\u2013154 (2004)","DOI":"10.1007\/s00493-004-0009-8"},{"key":"7_CR15","doi-asserted-by":"crossref","unstructured":"Hallgren, S.: Polynomial-time quantum algorithms for Pell\u2019s equation and the principal ideal problem. In: Proceedings of the 34th Annual ACM Symposium on Theory of computing, pp. 653\u2013658 (2002)","DOI":"10.1145\/509907.510001"},{"key":"7_CR16","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1109\/SFCS.2000.892139","volume-title":"Proc. of the 41st Annual Symposium on Foundations of Computer Science (FOCS 2000)","author":"L. Hales","year":"2000","unstructured":"Hales, L., Hallgren, S.: An improved quantum Fourier transform algorithm and applications. In: Proc. of the 41st Annual Symposium on Foundations of Computer Science (FOCS 2000), pp. 515\u2013525. IEEE Computer Society, Los Alamitos (2000)"},{"key":"7_CR17","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: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pp. 604\u2013617 (2006)","DOI":"10.1145\/1132516.1132603"},{"key":"#cr-split#-7_CR18.1","unstructured":"H??yer, P.: Efficient Quantum Transforms (February 1997);"},{"key":"#cr-split#-7_CR18.2","unstructured":"Arxiv preprint quant-ph\/9702028"},{"issue":"4","key":"7_CR19","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1137\/S009753970139450X","volume":"32","author":"S. Hallgren","year":"2003","unstructured":"Hallgren, S., Russell, A., Ta-Shma, A.: The hidden subgroup problem and quantum computation using group representations. SIAM Journal on Computing\u00a032(4), 916\u2013934 (2003)","journal-title":"SIAM Journal on Computing"},{"key":"7_CR20","volume-title":"Endliche Gruppen","author":"B. Huppert","year":"1983","unstructured":"Huppert, B.: Endliche Gruppen, vol.\u00a01. Springer, Heidelberg (1983)"},{"key":"7_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1007\/978-3-540-70918-3_50","volume-title":"STACS 2007","author":"G. Ivanyos","year":"2007","unstructured":"Ivanyos, G., Sanselme, L., Santha, M.: An efficient algorithm for hidden subgroup problem in extraspecial groups. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol.\u00a04393, pp. 586\u2013597. Springer, Heidelberg (2007)"},{"issue":"6","key":"7_CR22","doi-asserted-by":"publisher","first-page":"1191","DOI":"10.1070\/RM1997v052n06ABEH002155","volume":"52","author":"A.Y.. Kitaev","year":"1997","unstructured":"Kitaev, A.Y.: Quantum computations: algorithms and error correction. Russian Math. Surveys\u00a052(6), 1191\u20131249 (1997)","journal-title":"Russian Math. Surveys"},{"issue":"1","key":"7_CR23","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); Also arxiv preprint quant\u2013ph\/0302112","journal-title":"SIAM Journal on Computing"},{"key":"7_CR24","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)"},{"key":"#cr-split#-7_CR25.1","unstructured":"Moore, C., Rockmore, D., Russell, A., Schulman, L.: The power of basis selection in Fourier sampling: hidden subgroup problems in affine groups. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1113???1122 (2004);"},{"key":"#cr-split#-7_CR25.2","unstructured":"Also arxiv preprint quant-ph\/0503095"},{"issue":"1","key":"7_CR26","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1142\/S0219749904000109","volume":"2","author":"M. Mosca","year":"2004","unstructured":"Mosca, M., Zalka, C.H.: Exact quantum Fourier transforms and discrete logarithm algorithms. International Journal of Quantum Information\u00a02(1), 91\u2013100 (2004); Also arxiv preprint quant\u2013ph\/0301093","journal-title":"International Journal of Quantum Information"},{"key":"7_CR27","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)"},{"issue":"3","key":"7_CR28","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1137\/S0097539703440678","volume":"33","author":"R. Regev","year":"2004","unstructured":"Regev, R.: Quantum computation and lattice problems. SIAM Journal on Computing\u00a033(3), 738\u2013760 (2004)","journal-title":"SIAM Journal on Computing"},{"key":"7_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1399","DOI":"10.1007\/11523468_113","volume-title":"Automata, Languages and Programming","author":"J. Radhakrishnan","year":"2005","unstructured":"Radhakrishnan, J., R\u00f6tteler, M., Sen, P.: On the power of random bases in fourier sampling: Hidden subgroup problem in the heisenberg group. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol.\u00a03580, pp. 1399\u20131411. Springer, Heidelberg (2005)"},{"key":"#cr-split#-7_CR30.1","unstructured":"Sen, P.: Random measurement bases, quantum state distinction and applications to the hidden subgroup problem. In: Proceedings of the 21st Annual IEEE Conference on Computational Complexity, pp. 274???287 (2006);"},{"key":"#cr-split#-7_CR30.2","unstructured":"Also arxiv preprint quant-ph\/0512085"},{"key":"7_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9458-7","volume-title":"Linear Representations of Finite Groups","author":"J.P. Serre","year":"1977","unstructured":"Serre, J.P.: Linear Representations of Finite Groups. Springer, Heidelberg (1977)"},{"issue":"5","key":"7_CR32","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"}],"container-title":["Lecture Notes in Computer Science","Mathematical Methods in Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-89994-5_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,26]],"date-time":"2021-09-26T08:21:52Z","timestamp":1632644512000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-89994-5_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008]]},"ISBN":["9783540899938","9783540899945"],"references-count":41,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-89994-5_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008]]}}}