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Synthesis of linear quantum stochastic systems via quantum feedback networks

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1. The document outlines a method for synthesizing linear quantum stochastic systems using quantum feedback networks. Small time delays allow approximating direct interactions with field-mediated interactions. 2. As an example, a quantum optical circuit is synthesized based on earlier work. Components are interconnected to approximate a desired system dynamics for small time delays. 3. In conclusion, linear quantum systems can be approximately synthesized by quantum feedback networks for small time delays, using field-mediated interactions to simulate direct interactions. Additional results are available in another paper.

Tecnologia
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Hendra I. Nurdin (ANU) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A
Outline of talk ,[object Object],[object Object],[object Object],[object Object]
Linear quantum stochastic systems ,[object Object],Non-commuting Wiener processes Quantum Brownian motion
Linear quantum stochastic systems x = ( q 1 ,p 1 ,q 2 ,p 2 ,…, q n ,p n ) T A 1 = w 1 +iw 2 A 2 = w 3 +iw 4 A m =w 2m-1 +iw 2m Y 1 = y 1 + i y 2 Y 2 = y 3 + i y 4 Y m’ = y 2m’-1 + i y 2m’ S Quadratic Hamiltonian Linear coupling operator Scattering matrix S B 1 B 2 B m
Synthesis of linear quantum systems ,[object Object],Wish to realize this system ( S , L , H ) ? ? ? ? ? ? Network synthesis Quantum network Input fields Output fields Input fields Output fields
An earlier synthesis theorem ,[object Object],[object Object],Nurdin, James & Doherty, SIAM J. Control. Optim., 48(4), pp. 2686–2718, 2009. G 1 G 2 G 3 G n H 12 H 23 H 13 H 2n H 3n H 1n G = ( S , L , H ) A(t) y(t)
Realization of direct coupling Hamiltonians ,[object Object],Complicated in general, are there alternatives?
Quantum feedback networks
Quantum feedback networks ,[object Object],[object Object]
Approximate direct interaction via field-mediated interactions ,[object Object],Feedback interconnections to approximate direct interactions
Model matrix
Concatenated model matrix In channel 1 In channel 2 Out channel 1 Out channel 2
Connecting input and output, and reduced Markov model (Out channel 1 connected to In channel 2) (Series product) Gough & James, Comm. Math. Phys. , 287, pp. 1109–1132, 2009; IEEE-TAC , 54(11), pp. 2530–2544, 2009
Synthesis via quantum feedback networks ,[object Object],[object Object]
Synthesis via quantum feedback networks ,[object Object]
Synthesis via quantum feedback networks ,[object Object],[object Object],[object Object],[object Object]
Synthesis example
Synthesis example Quantum optical circuit based on Nurdin, James & Doherty, SIAM J. Control. Optim., 48(4), pp. 2686–2718, 2009.
Concluding remarks ,[object Object],[object Object],[object Object],[object Object]
That’s all folks THANK YOU FOR LISTENING!
From linear quantum stochastic systems to cavity QED systems Linear quantum stochastic system Cavity QED system

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Synthesis of linear quantum stochastic systems via quantum feedback networks

  • 1. Hendra I. Nurdin (ANU) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A
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  • 4. Linear quantum stochastic systems x = ( q 1 ,p 1 ,q 2 ,p 2 ,…, q n ,p n ) T A 1 = w 1 +iw 2 A 2 = w 3 +iw 4 A m =w 2m-1 +iw 2m Y 1 = y 1 + i y 2 Y 2 = y 3 + i y 4 Y m’ = y 2m’-1 + i y 2m’ S Quadratic Hamiltonian Linear coupling operator Scattering matrix S B 1 B 2 B m
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  • 12. Concatenated model matrix In channel 1 In channel 2 Out channel 1 Out channel 2
  • 13. Connecting input and output, and reduced Markov model (Out channel 1 connected to In channel 2) (Series product) Gough & James, Comm. Math. Phys. , 287, pp. 1109–1132, 2009; IEEE-TAC , 54(11), pp. 2530–2544, 2009
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  • 18. Synthesis example Quantum optical circuit based on Nurdin, James & Doherty, SIAM J. Control. Optim., 48(4), pp. 2686–2718, 2009.
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  • 20. That’s all folks THANK YOU FOR LISTENING!
  • 21. From linear quantum stochastic systems to cavity QED systems Linear quantum stochastic system Cavity QED system

Notas do Editor

  1. I am now going to introduce a class of quantum systems that are called linear quantum stochastic systems, these types of systems appear in quantum optics. Starting with a very simple example of such a system: An optical cavity (explain optical cavity).
  2. More general linear quantum stochastic systems are as shown in the following. Explain figure, especially quadratures of A i . Some outputs may be ignored, thus number of outputs need not be equal to the number of outputs
  3. Port strategy from classical network synthesis
  4. Spare slide, whip out for any necessary additional explanations