Exponential stochastic stabilization of a two-level quantum system via strict Lyapunov control

Gerardo Cardona 1 Alain Sarlette 2 Pierre Rouchon 2
2 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, MINES ParisTech - École nationale supérieure des mines de Paris, SU - Sorbonne Université, Inria de Paris
Abstract : This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian measurement operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the measurement operator. Previous work has proposed state feed-back that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous measurement output, our controller only depends on the single coordinate along the measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future
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https://hal.inria.fr/hal-01946780
Contributor : Alain Sarlette <>
Submitted on : Thursday, December 6, 2018 - 1:18:40 PM
Last modification on : Wednesday, May 15, 2019 - 3:35:31 AM
Long-term archiving on : Thursday, March 7, 2019 - 1:34:59 PM

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  • HAL Id : hal-01946780, version 1

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Gerardo Cardona, Alain Sarlette, Pierre Rouchon. Exponential stochastic stabilization of a two-level quantum system via strict Lyapunov control. CDC 2018 - 57th IEEE Conference on Decision and Control, Dec 2018, Miami, United States. ⟨hal-01946780⟩

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