Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control

Abstract

In this paper we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment or by non Hermitian measurements, there is no need for feedback control to accomplish the task. Constructive necessary and sufficient conditions on the form of the open-loop controller can be provided in this case. When open-loop control is not sufficient, filtering-based feedback control laws steering the evolution towards a target pure state are provided, which generalize those available in the literature.

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• Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization
• Information flow and error scaling for fully-quantum control
• On stability of quantum trajectories and their Cesaro mean
• A proposal of adaptive parameter tuning for robust stabilizing control of $N$--level quantum angular momentum systems
• Stabilization via feedback switching for quantum stochastic dynamics
• Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation