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Continuous-time quantum error correction with noise-assisted quantum feedback

(2019) IFAC PAPERSONLINE. 52(16). p.198-203
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Abstract
We address the standard quantum error correction using the three-qubit bit-flip code, yet in continuous-time. This entails rendering a target manifold of quantum states globally attractive. Previous feedback designs could feature spurious equilibria, or resort to discrete kicks pushing the system away from these equilibria to ensure global asymptotic stability. We present a new approach that consists of introducing controls driven by Brownian motions. Unlike the previous methods, the resulting closed-loop dynamics can be shown to stabilize the target manifold exponentially. We further present a reduced-order filter formulation with classical probabilities. The exponential property is important to quantify the protection induced by the closed-loop error-correction dynamics against disturbances. We study numerically the performance of this control law and of the reduced filter. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
Keywords
Quantum control, quantum error correction, stochastic systems, Lyapunov, method

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Please use this url to cite or link to this publication:

MLA
Cardona, Gerardo, et al. “Continuous-Time Quantum Error Correction with Noise-Assisted Quantum Feedback.” IFAC PAPERSONLINE, vol. 52, no. 16, Elsevier, 2019, pp. 198–203.
APA
Cardona, G., Sarlette, A., & Rouchon, P. (2019). Continuous-time quantum error correction with noise-assisted quantum feedback. In IFAC PAPERSONLINE (Vol. 52, pp. 198–203). Amsterdam: Elsevier.
Chicago author-date
Cardona, Gerardo, Alain Sarlette, and Pierre Rouchon. 2019. “Continuous-Time Quantum Error Correction with Noise-Assisted Quantum Feedback.” In IFAC PAPERSONLINE, 52:198–203. Amsterdam: Elsevier.
Chicago author-date (all authors)
Cardona, Gerardo, Alain Sarlette, and Pierre Rouchon. 2019. “Continuous-Time Quantum Error Correction with Noise-Assisted Quantum Feedback.” In IFAC PAPERSONLINE, 52:198–203. Amsterdam: Elsevier.
Vancouver
1.
Cardona G, Sarlette A, Rouchon P. Continuous-time quantum error correction with noise-assisted quantum feedback. In: IFAC PAPERSONLINE. Amsterdam: Elsevier; 2019. p. 198–203.
IEEE
[1]
G. Cardona, A. Sarlette, and P. Rouchon, “Continuous-time quantum error correction with noise-assisted quantum feedback,” in IFAC PAPERSONLINE, Tech Univ Wien, Vienna, AUSTRIA, 2019, vol. 52, no. 16, pp. 198–203.
@inproceedings{8640942,
  abstract     = {{We address the standard quantum error correction using the three-qubit bit-flip code, yet in continuous-time. This entails rendering a target manifold of quantum states globally attractive. Previous feedback designs could feature spurious equilibria, or resort to discrete kicks pushing the system away from these equilibria to ensure global asymptotic stability. We present a new approach that consists of introducing controls driven by Brownian motions. Unlike the previous methods, the resulting closed-loop dynamics can be shown to stabilize the target manifold exponentially. We further present a reduced-order filter formulation with classical probabilities. The exponential property is important to quantify the protection induced by the closed-loop error-correction dynamics against disturbances. We study numerically the performance of this control law and of the reduced filter. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.}},
  author       = {{Cardona, Gerardo and Sarlette, Alain and Rouchon, Pierre}},
  booktitle    = {{IFAC PAPERSONLINE}},
  issn         = {{2405-8963}},
  keywords     = {{Quantum control,quantum error correction,stochastic systems,Lyapunov,method}},
  language     = {{eng}},
  location     = {{Tech Univ Wien, Vienna, AUSTRIA}},
  number       = {{16}},
  pages        = {{198--203}},
  publisher    = {{Elsevier}},
  title        = {{Continuous-time quantum error correction with noise-assisted quantum feedback}},
  url          = {{http://dx.doi.org/10.1016/j.ifacol.2019.11.778}},
  volume       = {{52}},
  year         = {{2019}},
}

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