Coherent quantum LQG control

Automatica

Volumn 45, Issue 8, 2009, Pages 1837-1846

  Nurdin, Hendra I ^a   James, Matthew R ^a   Petersen, Ian R ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Linear control systems; Linear quadratic regulators; Quantum control; Quantum systems; Stochastic control

Indexed keywords

ALTERNATING PROJECTIONS; CLASSICAL CONTROLLERS; CONTROL SCHEMES; CONTROLLER DESIGNS; DEGREES OF FREEDOM; INDIRECT MEASUREMENTS; LINEAR CONSTRAINTS; LINEAR CONTROLLERS; LINEAR QUADRATIC REGULATORS; LINEAR STOCHASTIC SYSTEM; LQG CONTROL; NON-LINEAR; NUMERICAL PROCEDURES; NUMERICAL SOLUTION; OPTIMAL CONTROL PROBLEM; PHYSICAL REALIZABILITY; PLANT OUTPUT; PROBLEM-BASED; QUANTUM CONTROL; QUANTUM SYSTEM; QUANTUM SYSTEMS; STOCHASTIC CONTROL;

CONTROL; ENGINEERING EXHIBITIONS; FEEDBACK; LINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; QUANTUM ELECTRONICS; QUANTUM OPTICS; RANDOM PROCESSES; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

CONTROLLERS;

EID: 67649607487     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2009.04.018     Document Type: Article

References (35)

1. Advanced Optimization Lab, McMaster University. (2006). SeDuMi v1.1R3. http://sedumi.mcmaster.ca/
2. Armen M.A., Au J.K., Stockton J.K., Doherty A.C., and Mabuchi H. Adaptive homodyne measurement of optical phase. Physical Review A 89 13 (2002) 133602
3. Bachor H.A., and Ralph T.C. A guide to experiments in quantum optics. 2nd ed. (2004), Wiley-VCH, Weinheim, Germany
4. Belavkin V.P. On the theory of controlling observable quantum systems. Automation and Remote Control 44 2 (1983) 178-188
5. Belavkin V.P. Continuous non-demolition observation, quantum filtering and optimal estimation. Quantum aspects of optical communication. Lecture notes in physics Vol. 45 (1991), Springer, Berlin 131-145
6. Bouten L., van Handel R., and James M.R. An introduction to quantum filtering. SIAM Journal on Control and Optimization 46 (2007) 2199-2241
7. Boyd S., and Vanderberghe L. Semidefinite programming relaxations of non-convex problems in control and combinatorial optimization. In: Paulraj A., Roywhcowdhury V., and Schaper C. (Eds). Communications, computation, control and signal processing - A Tribute to Thomas Kailath (1997), Kluwer Academic Publishers, New York
8. Doherty A.C., and Jacobs K. Feedback-control of quantum systems using continuous state-estimation. Physical Review A 60 (1999) 2700. quant-ph/9812004
9. Edwards, S.C., & Belavkin, V.P. 2005. Optimal quantum filtering and quantum feedback control. http://arxiv.org/pdf/quant-ph/0506018
10. Gardiner C., and Zoller P. Quantum noise: A handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics. 2nd ed. Springer series in synergetics (2000), Springer
11. Gough J., and van Handel R. Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode. Journal of Statistical Physics 127 3 (2007) 575-607
12. Henrion D., and Lasserre J.B. Convergent relaxations of polynomial matrix inequalities and static output feedback. IEEE Transactions on Automatic Control 51 2 (2006) 192-202
13. Hol, C. W. J., & Scherer, C. (2004). Sum of squares relaxations for polynomial semidefinite programming. In Proc. 16th international symp. mathematical theory and networks
14. Hudson R.L., and Parthasarathy K.R. Quantum Ito's formula and stochastic evolution. Communications in Mathematical Physics 93 (1984) 301-323
15. Jacobs B.C., Pittman T.B., and Franson J.D. Quantum relays and noise suppression using linear optics. Physical Review A 66 (2002) 052307
16. ∞ control of linear quantum stochastic systems. IEEE Transactions on Automatic Control 53 8 (2008) 1787-1803
17. Knill E., Laflamme R., and Milburn G.J. A scheme for efficient quantum computation with linear optics. Nature 409 (2001) 46-52
18. Kojima, M. (2003). Sums of squares relaxations of polynomial semidefinite programs. Technical report B-397. Dept. Math. Comp. Sci., Tokyo Institute of Technology
19. Kok P., Williams C.P., and Dowling J.P. The construction of a quantum repeater with linear optics. Physical Review A 68 (2003) 022301
20. Lasserre J.B. Global optimization with polynomials and the problem of moments. SIAM Journal on Optimization 11 3 (2001) 796-817
21. Linblad G. Brownian motion of harmonic oscillators: Existence of a subdynamics. Journal of Mathematical Physics 39 5 (1998) 2763-2780
22. Löfberg, J. (2004). Yalmip : A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD conference
23. Mabuchi H. Coherent-feedback quantum control with a dynamic compensator. Physical Review A 78 (2008) 032323
24. Merzbacher E. Quantum mechanics. 3rd ed. (1998), Wiley, New York
25. Nesterov Y., and Nemirovskii A. Interior-point polynomial algorithms in convex programming (1994), SIAM, Philadelphia
26. Nielsen M.A., and Chuang I.L. Quantum computation and quantum information (2000), Cambridge University Press, Cambridge
27. Nurdin, H. I., James, M. R., & Doherty, A. C. (2009). Network synthesis of linear dynamical quantum stochastic systems. SIAM Journal on Control and Optimization (in press). http://arxiv.org/abs/0806.4448 (preprint)
28. Orsi, R. (2005). LMIRank: Software for rank constrained LMI problems. http://rsise.anu.edu.au/~robert/lmirank/
29. Orsi R., Helmke U., and Moore J.B. A Newton-like method for solving rank constrained linear matrix inequalities. Automatica Journal of IFAC 42 11 (2006) 1875-1882 Extended version available at R. Orsi's homepage
30. Parthasarathy K.R. An introduction to quantum stochastic calculus (1992), Birkhauser, Berlin
31. Scherer C., Gahinet P., and Chilali M. Multiobjective output-feedback control via LMI optimization. IEEE Transactions on Automatic Control 42 7 (1997) 896-911
32. Shaiju, A. J., Petersen, I. R., & James, M. R. (2007). Guaranteed cost LQG control of uncertain linear stochastic quantum systems. In Proceedings of the 2007 American control conference
33. Shor N.Z. Dual quadratic estimates in polynomial and boolean programming. Annals of Operations Research 25 (1990) 163-168
34. The Mathworks, Inc. Optimization toolbox 3: User's guide. 9th printing ed. (2007), The Mathworks, Inc.
35. Wiseman H., and Milburn G.J. Quantum theory of optical feedback via homodyne detection. Physical Review Letters 70 5 (1993) 548-551