We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a Quantum Non-Demolition (QND) 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 QND 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.
Dynamic Programming Principle and Stabilization for Mean-Field Quantum Filtering Systems
Université Paris-Saclay, CentraleSupélec（巴黎萨克雷大学，中央理工-高等电力学院）；University of Florida（佛罗里达大学）；CNRS, L2S, Université Paris-Saclay, CentraleSupélec（法国国家科学研究中心，L2S实验室，巴黎萨克雷大学，中央理工-高等电力学院）；Shanghai Frontiers Science Center of AI and DL NYU-ECNU Institute of Mathematical Sciences NYU Shanghai（上海人工智能前沿科学中心，纽约大学-华东师范大学数学科学研究所，纽约大学上海校区）
