Skip to main content
SpringerLink
Log in

Control of Quantum Systems

Encyclopedia of Systems and Control

  • 960 Accesses

Abstract

Quantum control theory is concerned with the control of systems whose dynamics are governed by the laws of quantum mechanics. Quantum control may take the form of open loop quantum control or quantum feedback control. Also, quantum feedback control may consist of measurement based feedback control, in which the controller is a classical system governed by the laws of classical physics. Alternatively, quantum feedback control may take the form of coherent feedback control in which the controller is a quantum system governed by the laws of quantum mechanics. In the area of open loop quantum control, questions of controllability along with optimal control and Lyapunov control methods are discussed. In the case of quantum feedback control, LQG and H ∞ control methods are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Notes

  1. 1.

    This work was supported by the Australian Research Council (ARC).

Bibliography

  • Albertini F, D’Alessandro D (2003) Notions of controllability for bilinear multilevel quantum systems. IEEE Trans Autom Control 48:1399–1403

    Article  MathSciNet  Google Scholar 

  • Bachor H, Ralph T (2004) A guide to experiments in quantum optics, 2nd edn. Wiley-VCH, Weinheim

    Book  Google Scholar 

  • Bertet P, Ong FR, Boissonneault M, Bolduc A, Mallet F, Doherty AC, Blais A, Vion D, Esteve D (2012) Circuit quantum electrodynamics with a nonlinear resonator. In: Dykman M (ed) Fluctuating nonlinear oscillators: from nanomechanics to quantum superconducting circuits. Oxford University Press, Oxford

    Google Scholar 

  • Breuer H, Petruccione F (2002) The theory of open quantum systems. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Brif C, Chakrabarti R, Rabitz H (2010) Control of quantum phenomena: past, present and future. New J Phys 12:075008

    Article  Google Scholar 

  • Bouten L, van Handel R, James M (2007) An introduction to quantum filtering. SIAM J Control Optim 46(6):2199–2241

    Article  MATH  MathSciNet  Google Scholar 

  • D’Alessandro D (2007) Introduction to quantum control and dynamics. Chapman & Hall/CRC, Boca Raton

    Book  Google Scholar 

  • Doherty A, Jacobs K (1999) Feedback-control of quantum systems using continuous state-estimation. Phys Rev A 60:2700–2711

    Article  Google Scholar 

  • Dong D, Petersen IR (2010) Quantum control theory and applications: a survey. IET Control Theory Appl 4(12):2651–2671

    Article  MathSciNet  Google Scholar 

  • Dong D, Lam J, Tarn T (2009) Rapid incoherent control of quantum systems based on continuous measurements and reference model. IET Control Theory Appl 3:161–169

    Article  MathSciNet  Google Scholar 

  • Gough J, James MR (2009) The series product and its application to quantum feedforward and feedback networks. IEEE Trans Autom Control 54(11):2530–2544

    Article  MathSciNet  Google Scholar 

  • Gough JE, James MR, Nurdin HI, Combes J (2012) Quantum filtering for systems driven by fields in single-photon states or superposition of coherent states. Phys Rev A 86:043819

    Article  Google Scholar 

  • Grigoriu A, Rabitz H, Turinici G (2013) Controllability analysis of quantum systems immersed within an engineered environment. J Math Chem 51(6):1548–1560

    Article  MATH  MathSciNet  Google Scholar 

  • James MR, Nurdin HI, Petersen IR (2008) H ∞ control of linear quantum stochastic systems. IEEE Trans Autom Control 53(8):1787–1803

    Article  MathSciNet  Google Scholar 

  • Kerckhoff J, Nurdin HI, Pavlichin DS, Mabuchi H (2010) Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction. Phys Rev Lett 105:040502

    Article  Google Scholar 

  • Khaneja N, Brockett R, Glaser S (2001) Time optimal control in spin systems. Phys Rev A 63:032308

    Article  Google Scholar 

  • Lloyd S (2000) Coherent quantum feedback. Phys Rev A 62:022108

    Article  MathSciNet  Google Scholar 

  • Merzbacher E (1970) Quantum mechanics, 2nd edn. Wiley, New York

    Google Scholar 

  • Mirrahimi M, van Handel R (2007) Stabilizing feedback controls for quantum systems. SIAM J Control Optim 46(2):445–467

    Article  MATH  MathSciNet  Google Scholar 

  • Mirrahimi M, Rouchon P, Turinici G (2005) Lyapunov control of bilinear Schrödinger equations. Automatica 41:1987–1994

    Article  MATH  MathSciNet  Google Scholar 

  • Nielsen M, Chuang I (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge, UK

    MATH  Google Scholar 

  • Nurdin HI, James MR, Petersen IR (2009) Coherent quantum LQG control. Automatica 45(8):1837–1846

    Article  MATH  MathSciNet  Google Scholar 

  • Polderman JW, Willems JC (1998) Introduction to mathematical systems theory: a behavioral approach. Springer, New York

    Book  Google Scholar 

  • Shaiju AJ, Petersen IR (2012) A frequency domain condition for the physical realizability of linear quantum systems. IEEE Trans Autom Control 57(8):2033–2044

    Article  MathSciNet  Google Scholar 

  • Shor P (1994) Algorithms for quantum computation: discrete logarithms and factoring. In: Goldwasser S (ed) Proceedings of the 35th annual symposium on the foundations of computer science. IEEE Computer Society, Los Alamitos, pp 124–134

    Chapter  Google Scholar 

  • Wang W, Schirmer SG (2010) Analysis of Lyapunov method for control of quantum states. IEEE Trans Autom Control 55(10):2259–2270

    Article  MathSciNet  Google Scholar 

  • Wiseman HM, Milburn GJ (2010) Quantum measurement and control. Cambridge University Press, Cambridge, UK

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT, Australia

    Ian Petersen

Authors
  1. Ian Petersen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ian Petersen .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag London

About this entry

Cite this entry

Petersen, I. (2014). Control of Quantum Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_147-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_147-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Control of Quantum Systems
    Published:
    31 December 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_147-2

  2. Original

    Control of Quantum Systems
    Published:
    10 October 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_147-1

Search

Navigation