{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:42:34Z","timestamp":1787319754756,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>The purpose of this paper is to develop a synthesis theory for linear dynamical quantum stochastic systems that are encountered in linear quantum optics and in phenomenological models of linear quantum circuits. In particular, such a theory will enable the systematic realization of coherent\/fully quantum linear stochastic controllers for quantum control, amongst other potential applications. We show how general linear dynamical quantum stochastic systems can be constructed by assembling an appropriate interconnection of one degree of freedom open quantum harmonic oscillators and, in the quantum optics setting, discuss how such a network of oscillators can be approximately synthesized or implemented in a systematic way from some linear and nonlinear quantum optical elements. An example is also provided to illustrate the theory.<\/jats:p>","DOI":"10.1137\/080728652","type":"journal-article","created":{"date-parts":[[2009,9,18]],"date-time":"2009-09-18T18:20:03Z","timestamp":1253298003000},"page":"2686-2718","source":"Crossref","is-referenced-by-count":120,"title":["Network Synthesis of Linear Dynamical Quantum Stochastic Systems"],"prefix":"10.1137","volume":"48","author":[{"given":"Hendra I.","family":"Nurdin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthew R.","family":"James","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew C.","family":"Doherty","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,9,18]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1109\/84.128057"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2003.1227"},{"key":"R3","first-page":"178","volume":"44","author":"Belavkin V.","year":"1983","journal-title":"Automat. 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Belavkin,\n                      Optimal quantum filtering and quantum feedback control\n                      , 2005, http:\/\/arxiv.org\/pdf\/quant-ph\/0506018."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.820065"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.929378"},{"key":"R13","unstructured":"H. I. Nurdin,\n                      Topics in classical and quantum linear stochastic systems\n                      , Ph.D. dissertation, The Australian National University, Canberra, 2007."},{"key":"R14","doi-asserted-by":"crossref","unstructured":"H. I. Nurdin, M. R. James, and I. R. Petersen,\n                      Quantum LQG control with quantum mechanical controllers\n                      , in Proceedings of the 17th IFAC World Congress, Seoul, South Korea, 2008, pp. 9922\u20139927.","DOI":"10.3182\/20080706-5-KR-1001.01679"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.04.018"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.29.1419"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.74.125314"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1038\/451664a"},{"key":"R19","unstructured":"B. D. O. Anderson and S. Vongpanitlerd,\n                      Network Analysis and Synthesis: A Modern Systems Theory Approach\n                      , Networks Series, Prentice-Hall, Englewood Cliffs, NJ, 1973."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1088\/0034-4885\/66\/7\/203"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"C. Gardiner and P. Zoller,\n                      Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics\n                      , Vol. 56, 2nd ed., Springer Ser. Synergetics, Springer, New York, 2000.","DOI":"10.1007\/978-3-662-04103-1"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1007\/BF01258530"},{"key":"R23","doi-asserted-by":"crossref","unstructured":"K. Parthasarathy,\n                      An Introduction to Quantum Stochastic Calculus\n                      , Birkhauser, Berlin, 1992.","DOI":"10.1007\/978-3-0348-0566-7"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/060651239"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.820063"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1063\/1.2354331"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/BF01198172"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1088\/1464-4266\/6\/1\/L01"},{"key":"R29","unstructured":"J. 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