{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T05:25:46Z","timestamp":1790227546111,"version":"4.1.0"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>A language L has a property tester if there exists a probabilistic algorithm that given an input x queries only a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L. We define a similar notion of quantum property testing and show that there exist languages with good quantum property testers but no good classical testers. We also show there exist languages which require a large number of queries even for quantumly testing.<\/jats:p>","DOI":"10.1137\/s0097539704442416","type":"journal-article","created":{"date-parts":[[2008,2,14]],"date-time":"2008-02-14T11:56:02Z","timestamp":1202990162000},"page":"1387-1400","source":"Crossref","is-referenced-by-count":29,"title":["Quantum Property Testing"],"prefix":"10.1137","volume":"37","author":[{"given":"Harry","family":"Buhrman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lance","family":"Fortnow","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ilan","family":"Newman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hein","family":"R\u00f6hrig","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,1,16]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"N. Alon,\n                      Testing subgraphs in large graphs\n                      , in Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, 2001, pp. 434\u2013441.","DOI":"10.1109\/SFCS.2001.959918"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(86)90019-2"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480102410973"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"N. Alon, E. Fischer, M. Krivelevich, and M. Szegedy,\n                      Efficient testing of large graphs\n                      , in Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, 1999, pp. 656\u2013666.","DOI":"10.1109\/SFFCS.1999.814642"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"N. Alon, I. Newman, M. Krivelevich, and M. Szegedy,\n                      Regular languages are testable with a constant number of queries\n                      , in Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, 1999, pp. 645\u2013655.","DOI":"10.1109\/SFFCS.1999.814641"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2004.04.008"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"N. Alon and A. Shapira,\n                      A characterization of the (natural) graph properties testable with one-sided error\n                      , in Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, 2005, pp. 429\u2013438.","DOI":"10.1109\/SFCS.2005.5"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"N. Alon and A. Shapira,\n                      Every monotone graph property is testable\n                      , in Proceedings of the 37th Annual ACM Symposium on Theory of Computing, 2005, pp. 128\u2013137.","DOI":"10.1145\/1060590.1060611"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"N. Alon and J. H. Spencer,\n                      The Probabilistic Method\n                      , 2nd ed., Wiley-Interscience, New York, 2000.","DOI":"10.1002\/0471722154"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1145\/502090.502097"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539796300933"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539796300921"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(93)90044-W"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"G. Brassard and P. H\u00f8yer,\n                      An\n                      exact quantum polynomial-time algorithm for Simon's problem\n                      , in Proceedings of the 5th Israeli Symposium on Theory of Computing and Systems (ISTCS'97), IEEE Computer Society Press, Los Alamitos, CA, 1997, pp. 12\u201323.","DOI":"10.1109\/ISTCS.1997.595153"},{"key":"R15","unstructured":"H. Buhrman, L. Fortnow, I. Newman, and H. R\u00f6hrig,\n                      Quantum property testing\n                      , in Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 2003, pp. 480\u2013488."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S009753970444199X"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"W. van Dam, F. Magniez, M. Mosca, and M. Santha,\n                      Self-testing of universal and fault-tolerant sets of quantum gates\n                      , in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, 2000, pp. 688\u2013696.","DOI":"10.1145\/335305.335402"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1999.1692"},{"key":"R19","first-page":"97","volume":"75","author":"Fischer E.","year":"2001","journal-title":"Bull. Eur. Assoc. Theor. Comput. Sci. EATCS"},{"key":"R20","unstructured":"E. Fischer,\n                      Testing graphs for colorability properties\n                      , in Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, 2001, pp. 873\u2013882."},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2003.11.004"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"E. Fischer and I. Newman,\n                      Testing of matrix properties\n                      , in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, 2001, pp. 286\u2013295.","DOI":"10.1145\/380752.380812"},{"key":"R23","doi-asserted-by":"crossref","unstructured":"K. Friedl, F. Magniez, M. Santha, and P. Sen,\n                      Quantum testers for hidden group properties\n                      , in Proceedings of the 28th International Symposium on Mathematical Foundations of Computer Science, 2003.","DOI":"10.1007\/978-3-540-45138-9_36"},{"key":"R24","doi-asserted-by":"crossref","unstructured":"O. Goldreich,\n                      Combinatorial property testing (a survey)\n                      , in Randomization Methods in Algorithm Design, AMS, Providence, RI, 1999, pp. 45\u201359.","DOI":"10.1090\/dimacs\/043\/04"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1145\/285055.285060"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-001-0078-7"},{"key":"R27","doi-asserted-by":"crossref","unstructured":"O. Goldreich and L. Trevisan,\n                      Three theorems regarding testing graph properties\n                      , in Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, 2001, pp. 460\u2013469.","DOI":"10.1109\/SFCS.2001.959922"},{"key":"R28","doi-asserted-by":"crossref","unstructured":"L. K. Grover,\n                      A fast quantum mechanical algorithm for database search\n                      , in Proceedings of the 28th ACM Symposium on Theory of Computing, 1996, pp. 212\u2013219.","DOI":"10.1145\/237814.237866"},{"key":"R29","doi-asserted-by":"crossref","unstructured":"L. Hales and S. Hallgren,\n                      An improved quantum Fourier transform algorithm and applications\n                      , in Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, 2000, pp. 515\u2013525.","DOI":"10.1109\/SFCS.2000.892139"},{"key":"R30","unstructured":"P. H\u00f8yer,\n                      Fourier Sampling\n                      , private communication, 2001."},{"key":"R31","doi-asserted-by":"crossref","unstructured":"D. Mayers and A. Yao,\n                      Quantum cryptography with imperfect apparatus\n                      , in Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, 1998, pp. 503\u2013509.","DOI":"10.1109\/SFCS.1998.743501"},{"key":"R32","unstructured":"M. A. Nielsen and I. L. Chuang,\n                      Quantum Computation and Quantum Information\n                      , Cambridge University Press, Cambridge, UK, 2000."},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10013"},{"key":"R34","unstructured":"D. Ron,\n                      Property testing\n                      , in Handbook of Randomized Computing, Comb. Optim. 9, S. Rajasekaran, P. M. Pardalos, J. H. Reif, and J. D. P. Rolim, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001, pp. 597\u2013649."},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793255151"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539795293172"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539796298637"},{"key":"R38","unstructured":"R. Solovay and A. Yao,\n                      Quantum Circuit Complexity and Universal Quantum Turing Machines\n                      , manuscript, 1996."},{"key":"R39","unstructured":"M. Szegedy,\n                      private communication\n                      , 1999."},{"key":"R40","doi-asserted-by":"crossref","unstructured":"A. C.C. Yao,\n                      Probabilistic computations: Toward a unified measure of complexity\n                      , in Proceedings of the 18th Annual IEEE Symposium on Foundations of Computer Science, 1977, pp. 222\u2013227.","DOI":"10.1109\/SFCS.1977.24"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539704442416","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:28:58Z","timestamp":1787336938000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539704442416"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":40,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/S0097539704442416"],"URL":"https:\/\/doi.org\/10.1137\/s0097539704442416","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}