A quantum algorithm for the Hidden Subgroup Problem over the group Z/p^{r}Z \rtimes Z/q^{s}Z is presented. This algorithm, which for certain parameters of the group qualifies as 'efficient', generalizes prior work on related semi-direct product groups.
@InProceedings{vandam_et_al:LIPIcs.TQC.2014.110, author = {van Dam, Wim and Dey, Siladitya}, title = {{Hidden Subgroup Quantum Algorithms for a Class of Semi-Direct Product Groups}}, booktitle = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)}, pages = {110--117}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-73-6}, ISSN = {1868-8969}, year = {2014}, volume = {27}, editor = {Flammia, Steven T. and Harrow, Aram W.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.110}, URN = {urn:nbn:de:0030-drops-48117}, doi = {10.4230/LIPIcs.TQC.2014.110}, annote = {Keywords: quantum algorithms, quantum complexity theory, computational group theory} }
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