{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T14:40:05Z","timestamp":1777300805124,"version":"3.51.4"},"reference-count":29,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2015,12,28]],"date-time":"2015-12-28T00:00:00Z","timestamp":1451260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"National Science Foundation","award":["CNS-0435060, grant CCR-0325197 and grant EN-CS-0329609"],"award-info":[{"award-number":["CNS-0435060, grant CCR-0325197 and grant EN-CS-0329609"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. Emerg. Technol. Comput. Syst."],"published-print":{"date-parts":[[2016,7,26]]},"abstract":"<jats:p>\n            In this article, the problem of synthesizing a general Hermitian quantum gate into a set of primary quantum gates is addressed. To this end, an extended version of the Jacobi approach for calculating the eigenvalues of Hermitian matrices in linear algebra is considered as the basis of the proposed synthesis method. The quantum circuit synthesis method derived from the Jacobi approach and its optimization challenges are described. It is shown that the proposed method results in multiple-control rotation gates around the\n            <jats:italic>y<\/jats:italic>\n            axis, multiple-control phase shift gates, multiple-control NOT gates, and a middle diagonal Hermitian matrix, which can be synthesized to multiple-control Pauli\n            <jats:italic>Z<\/jats:italic>\n            gates. Using the proposed approach, it is shown how multiple-control\n            <jats:italic>U<\/jats:italic>\n            gates, where\n            <jats:italic>U<\/jats:italic>\n            is a single-qubit Hermitian quantum gate, can be implemented using a linear number of elementary gates in terms of circuit lines with the aid of one auxiliary qubit in an arbitrary state.\n          <\/jats:p>","DOI":"10.1145\/2794263","type":"journal-article","created":{"date-parts":[[2015,12,30]],"date-time":"2015-12-30T13:13:41Z","timestamp":1451481221000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Quantum-Logic Synthesis of Hermitian Gates"],"prefix":"10.1145","volume":"12","author":[{"given":"Mona","family":"Arabzadeh","sequence":"first","affiliation":[{"name":"Amirkabir University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mahboobeh","family":"Houshmand","sequence":"additional","affiliation":[{"name":"Amirkabir University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mehdi","family":"Sedighi","sequence":"additional","affiliation":[{"name":"Amirkabir University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Morteza Saheb","family":"Zamani","sequence":"additional","affiliation":[{"name":"Amirkabir University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,12,28]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Asia and South Pacific Design Automation Conference. 849--854","author":"Arabzadeh M."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.52.3457"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.71.052330"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.12.046"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.5555\/2011572.2011575"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/5992.908999"},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","unstructured":"V. Danos E. Kashefi P. Panangaden and S. Perdrix. 2009. Extended Measurement Calculus. Semantic Techniques in Quantum Computation.  V. Danos E. Kashefi P. Panangaden and S. Perdrix. 2009. Extended Measurement Calculus. Semantic Techniques in Quantum Computation.","DOI":"10.1017\/CBO9781139193313.008"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02650179"},{"key":"e_1_2_1_9_1","unstructured":"G. H. Golub and C. F. Van Loan. 1996. Matrix Computations. Vol. 3. JHUP.  G. H. Golub and C. F. Van Loan. 1996. Matrix Computations. Vol. 3. JHUP."},{"key":"e_1_2_1_10_1","unstructured":"M. Grassl. 2008. Circuits for quantum error-correction codes. http:\/\/iaks-www.ira.uka.de\/home\/grassl\/QECC\/circuits\/.  M. Grassl. 2008. 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Non-Hermitian quantum gates are more common than Hermitian quantum gates. E-Print Quant-Ph\/1309.4037v1 (2013).  A. Pathak. 2013. Non-Hermitian quantum gates are more common than Hermitian quantum gates. E-Print Quant-Ph\/1309.4037v1 (2013)."},{"key":"e_1_2_1_19_1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.26421\/QIC11.3-4-6","article-title":"Block-based quantum-logic synthesis","volume":"11","author":"Saeedi M.","year":"2011","journal-title":"Quantum Information and Computation"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2005.855930"},{"key":"e_1_2_1_21_1","doi-asserted-by":"crossref","first-page":"5","DOI":"10.26421\/QIC8.5-6-8","article-title":"On the CNOT-cost of Toffoli gates","volume":"9","author":"Shende V. V.","year":"2009","journal-title":"Quantum Information and Computation"},{"key":"e_1_2_1_22_1","unstructured":"V. V. Shende I. L. Markov and S. S. Bullock. 2004. Smaller two-qubit circuits for quantum communication and computation. Design Automation and Test in Europe (2004) 980--985.   V. V. Shende I. L. Markov and S. S. Bullock. 2004. Smaller two-qubit circuits for quantum communication and computation. Design Automation and Test in Europe (2004) 980--985."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539795293172"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.177902"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.69.032315"},{"key":"e_1_2_1_26_1","unstructured":"F. Vatan and C. P. Williams. 2004b. Realization of a general three-qubit quantum gate. E-Print Quant-Ph\/0401178 (2004).  F. Vatan and C. P. Williams. 2004b. Realization of a general three-qubit quantum gate. 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