We consider a class of pure-state preparation problems for stochastic quantum dynamics, by means of Hamiltonian control, continuous measurement and quantum feedback, in the presence of a Markovian environment. We prove that, whenever suitable dissipative effects are induced either by the unmonitored environment or by continuous-time measurements, open-loop time-invariant control is in principle sufficient to achieve stabilization of the target state (in probability). When this is not sufficient, we show that state stabilization can be attained for a wide class of models by the addition of a switching, filtering-based feedback control Hamiltonian.
We consider a class of pure-state preparation problems for stochastic quantum dynamics, by means of Hamiltonian control, continuous measurement and quantum feedback, in the presence of a Markovian environment. We prove that, whenever suitable dissipative effects are induced either by the unmonitored environment or by continuous-time measurements, open-loop time-invariant control is in principle sufficient to achieve stabilization of the target state (in probability). When this is not sufficient, we show that state stabilization can be attained for a wide class of models by the addition of a switching, filtering-based feedback control Hamiltonian.
We consider a class of pure-state preparation problems for stochastic quantum dynamics, by means of Hamiltonian control, continuous measurement and quantum feedback, in the presence of a Markovian environment. We prove that, whenever suitable dissipative effects are induced either by the unmonitored environment or by continuous-time measurements, open-loop time-invariant control is in principle sufficient to achieve stabilization of the target state (in probability). When this is not sufficient, we show that state stabilization can be attained for a wide class of models by the addition of a switching, filtering-based feedback control Hamiltonian.
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, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control.
We propose a new method for pure-state and subspace preparation in quantum systems, which employs the output of a continuous measurement process and switching dissipative control to improve convergence speed, as well as robustness with respect to the initial conditions. In particular, we prove that the proposed closed-loop strategy makes the desired target globally asymptotically stable both in mean and almost surely, and we show it compares favorably against a time-based and a state-based switching control law, with significant improvements in the case of faulty initialization.
Abstract. In this work we analyze and bound the effect of modeling errors on the stabilization of pure states or subspaces for quantum stochastic evolutions. Different approaches are used for open-loop and feedback control protocols. For both, we highlight the key role of dynamical invariance of the target: if the perturbation preserves invariance, it is possible to prove that it also preserves its attractivity, under some additional assumptions. In addition, we prove boundedness in mean of the solutions of perturbed systems under open-loop protocols. For the feedback strategies, in the general case without assumptions on invariance, we provide bounds on the perturbation effect in expectation and in probability, as well as specific bounds for nondemolition nominal systems.
This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems, with the main analysis focused on finite-dimensional systems governed by diffusive stochastic master equations. We introduce the relevant state-space, invariant-subspace, and quantum non-demolition structures, interpret quantum filtering as nonlinear observer dynamics, and review open-loop asymptotics, filter stability, state-feedback stabilization, robustness, and reduced-order observer-based control. Particular emphasis is placed on a recurrence--contraction framework, in which Hamiltonian feedback removes non-target invariant obstructions while measurement-induced dynamics provide local exponential contraction. Although the detailed analysis is developed for finite-dimensional diffusive models, the underlying measurement--estimation--feedback architecture is relevant across a broad range of quantum platforms. We further discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics, practical stability, optimal control, and learning-based design. By organizing these developments around invariance, estimation, recurrence, and contraction, the review provides a tutorial bridge between measurement-based quantum feedback and nonlinear stochastic control.
We propose a new method for pure-state and subspace preparation in quantum systems, which employs the output of a continuous measurement process and switching dissipative control to improve convergence speed, as well as robustness with respect to the initial conditions. In particular, we prove that the proposed closed-loop strategy makes the desired target globally asymptotically stable both in mean and almost surely, and we show it compares favorably against a time-based and a state-based switching control law, with significant improvements in the case of faulty initialization.