{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:48:10Z","timestamp":1776127690846,"version":"3.50.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2003,10]]},"abstract":"<jats:p> We present two methods for the construction of quantum circuits for quantum error- correcting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC encoding k qudits into n qudits, the resulting quantum circuit has O(n(n - k)) gates. The running time of the classical algorithm to compute the quantum circuit is O(n(n - k)<jats:sup>2<\/jats:sup>). <\/jats:p>","DOI":"10.1142\/s0129054103002011","type":"journal-article","created":{"date-parts":[[2003,11,24]],"date-time":"2003-11-24T04:26:19Z","timestamp":1069647979000},"page":"757-775","source":"Crossref","is-referenced-by-count":82,"title":["EFFICIENT QUANTUM CIRCUITS FOR NON-QUBIT QUANTUM ERROR-CORRECTING CODES"],"prefix":"10.1142","volume":"14","author":[{"given":"MARKUS","family":"GRASSL","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Algorithmen und Kognitive Systeme, Universit\u00e4t Karlsruhe, Am Fasanengarten 5, 76 128 Karlsruhe, Germany"},{"name":"The Mathematical Sciences Research Institute, 1000 Centennial Drive, #5070, Berkeley, CA 94720-5070, USA"}]},{"given":"MARTIN","family":"R\u00d6TTELER","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Algorithmen und Kognitive Systeme, Universit\u00e4t Karlsruhe, Am Fasanengarten 5, 76 128 Karlsruhe, Germany"},{"name":"Department of Combinatorics and Optimization,  Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada,  N2L 3G1, Canada"}]},{"given":"THOMAS","family":"BETH","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Algorithmen und Kognitive Systeme, Universit\u00e4t Karlsruhe, Am Fasanengarten 5, 76 128 Karlsruhe, Germany"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1063\/1.3062610"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01857727"},{"key":"rf12","unstructured":"M.\u00a0Grassl, Mathematics of Quantum Computation, eds. R. K.\u00a0Brylinski and G.\u00a0Chen (Chapman & Hall\/CRC, Boca Raton, 2002)\u00a0pp. 223\u2013252."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-64981-3"},{"key":"rf19","volume-title":"Finite Fields","author":"Jungnickel D.","year":"1993"},{"key":"rf23","volume-title":"Finite Fields","author":"Lidl R.","year":"1983"},{"key":"rf24","volume-title":"The Theory of Error\u2013Correcting Codes","author":"MacWilliams F. J.","year":"1977"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/016"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.77.793"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-10003-2_104"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19821090103"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054103002011","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:37:46Z","timestamp":1565123866000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054103002011"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,10]]},"references-count":11,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,10]]}},"alternative-id":["10.1142\/S0129054103002011"],"URL":"https:\/\/doi.org\/10.1142\/s0129054103002011","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,10]]}}}