{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T20:24:37Z","timestamp":1790799877193,"version":"4.1.0"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2013,5,24]],"date-time":"2013-05-24T00:00:00Z","timestamp":1369353600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2013,10]]},"DOI":"10.1007\/s11128-013-0588-7","type":"journal-article","created":{"date-parts":[[2013,5,23]],"date-time":"2013-05-23T13:24:10Z","timestamp":1369315450000},"page":"3149-3166","source":"Crossref","is-referenced-by-count":1,"title":["The rational approximations of the unitary groups"],"prefix":"10.1007","volume":"12","author":[{"given":"Ming-Xing","family":"Luo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yun","family":"Deng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiu-Bo","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi-Xian","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2013,5,24]]},"reference":[{"issue":"1","key":"588_CR1","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1103\/RevModPhys.38.95","volume":"38","author":"C Itzykson","year":"1966","unstructured":"Itzykson, C., Nauenberg, M.: Unitary groups: representations and decompostions. Rev. Mod. Phys. 38(1), 95\u2013120 (1966)","journal-title":"Rev. Mod. Phys."},{"key":"588_CR2","doi-asserted-by":"crossref","first-page":"3457","DOI":"10.1103\/PhysRevA.52.3457","volume":"52","author":"A Barenco","year":"1995","unstructured":"Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N.H., Shor, P.W., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457 (1995)","journal-title":"Phys. Rev. A"},{"key":"588_CR3","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1098\/rspa.1985.0070","volume":"400","author":"D Deutsch","year":"1985","unstructured":"Deutsch, D.: Quantum-theory, the Church-turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97\u2013117 (1985)","journal-title":"Proc. R. Soc. Lond. A"},{"key":"588_CR4","doi-asserted-by":"crossref","first-page":"1484","DOI":"10.1137\/S0097539795293172","volume":"26","author":"PW Shor","year":"1997","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484\u20131509 (1997)","journal-title":"SIAM J. Comput."},{"key":"588_CR5","doi-asserted-by":"crossref","first-page":"4709","DOI":"10.1103\/PhysRevLett.79.4709","volume":"79","author":"LK Grover","year":"1997","unstructured":"Grover, L.K.: Quantum computer can search arbitarily large databases by a single querry. Phys. Rev. Lett. 79, 4709\u20134712 (1997)","journal-title":"Phys. Rev. Lett."},{"key":"588_CR6","doi-asserted-by":"crossref","first-page":"3408","DOI":"10.1103\/PhysRevLett.80.3408","volume":"80","author":"IL Chuang","year":"1998","unstructured":"Chuang, I.L., Gershenfeld, N., Kubinec, M.: Experimental implementation of fast quantum searching. Phys. Rev. Lett. 80, 3408\u20133411 (1998)","journal-title":"Phys. Rev. Lett."},{"key":"588_CR7","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1038\/30687","volume":"393","author":"JA Jones","year":"1998","unstructured":"Jones, J.A., Mosca, M., Hansen, R.H.: Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344\u2013346 (1998)","journal-title":"Nature"},{"key":"588_CR8","doi-asserted-by":"crossref","first-page":"060302","DOI":"10.1103\/PhysRevA.76.060302","volume":"76","author":"N Yoran","year":"2007","unstructured":"Yoran, N., Short, A.J.: Classical simulability and the significance of modular exponentiation in Shor\u2019s algorithm. Phys. Rev. A 76, 060302 (2007)","journal-title":"Phys. Rev. A"},{"key":"588_CR9","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1088\/1367-2630\/9\/5\/146","volume":"9","author":"DE Browne","year":"2007","unstructured":"Browne, D.E.: Efficient classical simulation of the quantum Fourier transform. New J. Phys. 9, 146 (2007)","journal-title":"New J. Phys."},{"key":"588_CR10","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/BF02650179","volume":"21","author":"R Feynman","year":"1982","unstructured":"Feynman, R.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467\u2013488 (1982)","journal-title":"Int. J. Theor. Phys."},{"key":"588_CR11","volume-title":"Principles of Numerical Analysis","author":"AS Householder","year":"1953","unstructured":"Householder, A.S.: Principles of Numerical Analysis. McGraw-Hill, New York (1953)"},{"key":"588_CR12","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1103\/PhysRevLett.73.58","volume":"73","author":"M Reck","year":"1994","unstructured":"Reck, M., Zeilinger, A., Bernstein, H.J., Bertani, P.: Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58 (1994)","journal-title":"Phys. Rev. Lett."},{"key":"588_CR13","doi-asserted-by":"crossref","first-page":"042330","DOI":"10.1103\/PhysRevA.81.042330","volume":"81","author":"NB Lovett","year":"2010","unstructured":"Lovett, N.B., Cooper, S., Everitt, M., Trevers, M., Kendon, V.: Universal quantum computation using the discrete-time quantum walk. Phys. Rev. A 81, 042330 (2010)","journal-title":"Phys. Rev. A"},{"key":"588_CR14","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1016\/j.tcs.2010.10.031","volume":"412","author":"Y Thibault","year":"2011","unstructured":"Thibault, Y., Sugimotob, A., Kenmochia, Y.: 3D discrete rotations using hinge angles. Theor. Comput. Sci. 412, 1378\u20131391 (2011)","journal-title":"Theor. Comput. Sci."},{"key":"588_CR15","doi-asserted-by":"crossref","first-page":"022323","DOI":"10.1103\/PhysRevA.74.022323","volume":"74","author":"PA Ivanov","year":"2006","unstructured":"Ivanov, P.A., Kyoseva, E.S., Vitanov, N.V.: Engineering of arbitrary $$U(N)$$ transformations by quantum householder reflections. Phys. Rev. A 74, 022323 (2006)","journal-title":"Phys. Rev. A"},{"key":"588_CR16","volume-title":"An Introduction to Diophantine Approximations","author":"JWS Cassels","year":"1953","unstructured":"Cassels, J.W.S.: An Introduction to Diophantine Approximations. Cambridge University Press, Cambridge (1953)"},{"key":"588_CR17","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1137\/050643878","volume":"30","author":"C Fraikin","year":"2008","unstructured":"Fraikin, C., Nesterov, Y., Van Dooren, P.: Optimizing the coupling between two isometric projections of matrices. SIAM J. Matrix Anal. Appl. 30, 324\u2013345 (2008)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"588_CR18","doi-asserted-by":"crossref","first-page":"287","DOI":"10.2307\/2320748","volume":"86","author":"PD Humke","year":"1979","unstructured":"Humke, P.D., Krajewski, L.L.: A characterization of circles which contain rational points. Am. Math. Mon. 86, 287\u2013290 (1979)","journal-title":"Am. Math. Mon."},{"key":"588_CR19","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1215\/S0012-7094-53-02004-3","volume":"20","author":"AJ Hoffman","year":"1953","unstructured":"Hoffman, A.J., Wielandt, W.: The variation of the spectrum. Duke Math. J. 20, 37\u201339 (1953)","journal-title":"Duke Math. J."},{"key":"588_CR20","first-page":"71","volume":"15","author":"R Bhatia","year":"1984","unstructured":"Bhatia, R., Davis, C.: A bound for the spectral variation of a unitary operator. Lin. Alg. Its Appl. 15, 71\u201376 (1984)","journal-title":"Lin. Alg. Its Appl."},{"issue":"189","key":"588_CR21","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0024-3795(93)90469-5","volume":"188","author":"L Elsner","year":"1993","unstructured":"Elsner, L., He, C.: Perturbation and interlace theorems for the unitary eigenvalue problem. Lin. Alg. Its Appl. 188(189), 207\u2013229 (1993)","journal-title":"Lin. Alg. Its Appl."},{"issue":"1","key":"588_CR22","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1215\/00127094-2008-046","volume":"145","author":"P Bourgade","year":"2008","unstructured":"Bourgade, P., Hughes, C.P., Nikeghbali, A.: The characteristic polynomial of a random unitary matrix: a probabilistic approach. Duke Math. J. 145(1), 45\u201369 (2008)","journal-title":"Duke Math. J."},{"key":"588_CR23","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1137\/050627563","volume":"29","author":"DA Bini","year":"2007","unstructured":"Bini, D.A., Eidelman, Y., Gohberg, I., Gemignani, L.: Fast QR eigenvalue algorithms for hessenberg matrices which are rank-one perturbations of unitary matrices. SIAM J. Matrix Anal. Appl. 29, 566\u2013585 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"588_CR24","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1137\/080725167","volume":"312","author":"CC Paige","year":"2009","unstructured":"Paige, C.C.: A useful form of unitary matrix obtained from any sequence of unit 2-norm $$N$$ -vectors. SIAM J. Matrix Anal. Appl. 312, 565\u2013583 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"588_CR25","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s002200000261","volume":"214","author":"JP Keating","year":"2000","unstructured":"Keating, J.P., Snaith, N.C.: Random matrix theory and $$z(1\/2+it)$$ . Commun. Math. Phys. 214, 57\u201389 (2000)","journal-title":"Commun. Math. Phys."},{"key":"588_CR26","doi-asserted-by":"crossref","first-page":"4235","DOI":"10.1088\/0305-4470\/27\/12\/028","volume":"27","author":"K Zyczkowski","year":"1994","unstructured":"Zyczkowski, K., Kus, M.: Random unitary matrices. J. Phys. A Math. Gen. 27, 4235 (1994)","journal-title":"J. Phys. A Math. Gen."},{"key":"588_CR27","first-page":"592","volume":"54","author":"F Mezzadri","year":"2007","unstructured":"Mezzadri, F.: How to generate random matrices from the classical compact groups. Notices AMS 54, 592\u2013604 (2007)","journal-title":"Notices AMS"},{"key":"588_CR28","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1137\/S0097539700377025","volume":"31","author":"L Valiant","year":"2002","unstructured":"Valiant, L.: Quantum circuits that can be simulated classically in polynomial time. SIAM J. Comput. 31, 1229\u20131254 (2002)","journal-title":"SIAM J. Comput."},{"key":"588_CR29","doi-asserted-by":"crossref","first-page":"032325","DOI":"10.1103\/PhysRevA.65.032325","volume":"65","author":"BM Terhal","year":"2002","unstructured":"Terhal, B.M., DiVincenzo, D.P.: Classical simulation of noninteracting-fermion quantum circuits. Phys. Rev. A 65, 032325 (2002)","journal-title":"Phys. Rev. A"},{"key":"588_CR30","doi-asserted-by":"crossref","first-page":"3089","DOI":"10.1098\/rspa.2008.0189","volume":"464","author":"R Jozsa","year":"2008","unstructured":"Jozsa, R., Miyake, A.: Matchgates and classical simulation of quantum circuits. Proc. R. Soc. A 464, 3089\u20133106 (2008)","journal-title":"Proc. R. Soc. A"},{"key":"588_CR31","unstructured":"Knill, E.: Fermionic linear optics and matchgates, http:\/\/www.arXiv.org\/abs\/quant-ph\/0108033 , (2001)"},{"key":"588_CR32","first-page":"216","volume":"5","author":"S Bravyi","year":"2005","unstructured":"Bravyi, S.: Lagrangian representation for fermionic linear optics. Quant. Inf. Comp. 5, 216\u2013238 (2005)","journal-title":"Quant. Inf. Comp."},{"key":"588_CR33","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1090\/conm\/482\/09419","volume":"482","author":"S Bravyi","year":"2009","unstructured":"Bravyi, S.: Contraction of matchgate tensor networks on nonplanar graphs. Contemp. Math. 482, 179\u2013211 (2009)","journal-title":"Contemp. Math."},{"key":"588_CR34","doi-asserted-by":"crossref","first-page":"131","DOI":"10.2307\/2323943","volume":"98","author":"H Liebeck","year":"1991","unstructured":"Liebeck, H., Osborne, A.: The generation of all rational orthogonal matrices. Am. Math. Mon. 98, 131\u2013133 (1991)","journal-title":"Am. Math. Mon."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-013-0588-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-013-0588-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-013-0588-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T03:39:13Z","timestamp":1559360353000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-013-0588-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,24]]},"references-count":34,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2013,10]]}},"alternative-id":["588"],"URL":"https:\/\/doi.org\/10.1007\/s11128-013-0588-7","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,24]]}}}