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Exponential stabilization of quantum systems under continuous non-demolition measurements

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 : We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a quantum measurement operator. In open-loop, the system converges to a random eigenstate of the measurement operator. The role of the feedback is to prepare a prescribed eigenstate with unit probability. To achieve this we introduce the use of Brownian motion to drive the unitary control actions; the feedback loop just adapts the 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, while relying on the open-loop dynamics to progressively reach the target. We prove exponential convergence towards the target eigenstate using standard stochastic Lyapunov methods. The feedback scheme and its stability analysis suggest the use of an approximate filter which only tracks the populations of the eigenstates of the measurement operator. Such reduced filters should play an increasing role towards advanced quantum technologies.
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Submitted on : Wednesday, December 4, 2019 - 9:40:30 PM
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Gerardo Cardona, Alain Sarlette, Pierre Rouchon. Exponential stabilization of quantum systems under continuous non-demolition measurements. Automatica, Elsevier, 2019, ⟨10.1016/j.automatica.2019.108719⟩. ⟨hal-02394692⟩

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