{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T23:19:44Z","timestamp":1782256784770,"version":"3.54.5"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J CIRCUIT SYST COMP"],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p> Because ternary computer has more superiority than other d-ary number systems, we focus on the investigation of ternary elementary quantum gates and the synthesis algorithm of ternary quantum logic circuits. Above all, Pauli operators and their matrices on qutrit are introduced. Then eight qutrit operators are selected as elementary operators and eight qutrit quantum logic gates are defined. Permutation groups are introduced to characterize the quantum gates and quantum logic circuits. Some important qutrit quantum logic gates are defined also, such as QNOT, QKCXi, EQKCXi, QSwap, QCNOT and EQCNOT. Based on these elementary gates, we prove two very important theorems: (1) all qutrit quantum reversible logic circuit can be generated by Xi gate and QKCXi gate; (2) all qutrit quantum reversible logic circuits can be generated by Xi gate and QCNOT gate. The two theorems indicate that any complicated qutrit quantum reversible circuit can be constructed by the simplest ternary quantum gate. This will greatly simplify the implementation difficulty of quantum circuit. Subsequently, we propose a synthesis algorithm for qutrit quantum reversible logic circuit, which is verified through simulation experiment by the computer program we have designed. <\/jats:p>","DOI":"10.1142\/s0218126615501212","type":"journal-article","created":{"date-parts":[[2015,7,2]],"date-time":"2015-07-02T00:03:39Z","timestamp":1435795419000},"page":"1550121","source":"Crossref","is-referenced-by-count":12,"title":["A Synthesis Method of Quantum Reversible Logic Circuit Based on Elementary Qutrit Quantum Logic Gates"],"prefix":"10.1142","volume":"24","author":[{"given":"Fuyou","family":"Fan","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P. R. China"},{"name":"School of Computer Science and Engineering, Yibin University, Yibin, Sichuan 644000, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guowu","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William N. N.","family":"Hung","sequence":"additional","affiliation":[{"name":"Synopsys Inc., Mountain View, California 94043, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2015,8,12]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1985.0070"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.48.1581"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01342185"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1989.0099"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1126\/science.261.5128.1569"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.62.052309"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1126\/science.270.5234.255"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.52.3457"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.74.4087"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.097901"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.77.022326"},{"key":"rf12","unstructured":"O.\u00a0Spaniol, Computer Arithmetic: Logic and Design (Jonh Wiley & Sons, Hoboken, New Jersey, 1981)\u00a0p. 125."},{"key":"rf13","unstructured":"M.\u00a0Nielsen and I.\u00a0Chuang, Quantum Computation and Quantum Information (Cambridge University, London, 2000)\u00a0p. 85."},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1992.0167"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1080\/09500349414552351"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/24\/013"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/38\/44\/006"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0731-3_1"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1038\/nphys1150"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1142\/S021974991000671X"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1109\/5992.908999"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.177902"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.93.130502"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.85.032331"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.87.012325"}],"container-title":["Journal of Circuits, Systems and Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218126615501212","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:15:09Z","timestamp":1565079309000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218126615501212"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,12]]},"references-count":25,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2015,8,12]]},"published-print":{"date-parts":[[2015,9]]}},"alternative-id":["10.1142\/S0218126615501212"],"URL":"https:\/\/doi.org\/10.1142\/s0218126615501212","relation":{},"ISSN":["0218-1266","1793-6454"],"issn-type":[{"value":"0218-1266","type":"print"},{"value":"1793-6454","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8,12]]}}}