Exponential stabilization of quantum systems under continuous non-demolition measurements

Gerardo Cardona 1 Alain Sarlette 2 Pierre Rouchon 2
2 QUANTIC - QUANTum Information Circuits
MINES ParisTech - École nationale supérieure des mines de Paris, ENS Paris - École normale supérieure - Paris, SU - Sorbonne Université, Inria de Paris
Abstract : We present a novel continuous-time control strategy to exponentially stabilize an eigenstateof a Quantum Non-Demolition (QND) measurement operator. In open-loop, the systemconverges to a random eigenstate of the measurement operator. The role of the feedback is toprepare a prescribed QND eigenstate with unit probability. To achieve this we introduce theuse of Brownian motion to drive the unitary control actions; the feedback loop just adaptsthe amplitude of this Brownian noise input as a function of the system state. Essentially, it“shakes” the system away from undesired eigenstates by applying strong noise there, whilerelying on the open-loop dynamics to progressively reach the target. We prove exponentialconvergence towards the target eigenstate using standard stochastic Lyapunov methods. Thefeedback scheme and its stability analysis suggest the use of an approximate filter which onlytracks the populations of the eigenstates of the measurement operator. Such reduced filtersshould play an increasing role towards advanced quantum technologies.
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Submitted on : Friday, December 6, 2019 - 4:47:11 PM
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Gerardo Cardona, Alain Sarlette, Pierre Rouchon. Exponential stabilization of quantum systems under continuous non-demolition measurements. Automatica, Elsevier, 2020, 112, pp.108719. ⟨10.1016/j.automatica.2019.108719⟩. ⟨hal-02397786⟩



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