Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control

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

General fixed points of quasi-local frustration-free quantum semigroups: from invariance to stabilization

We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints. Our central result is a linear-algebraic necessary and sufficient condition for a generic (full-rank) target state to be frustration-free quasi-locally stabilizable, along with an explicit procedure for constructing Markovian dynamics that achieve stabilization. If the target state is not full-rank, we establish sufficiency under an additional condition, which is naturally motivated by consistency with pure-state stabilization results yet provably not necessary in general. Several applications are discussed, of relevance to both dissipative quantum engineering and information processing, and non-equilibrium quantum statistical mechanics. In particular, we show that a large class of graph product states (including arbitrary thermal graph states) as well as Gibbs states of commuting Hamiltonians are frustration-free stabilizable relative to natural quasi-locality constraints. Likewise, we provide explicit examples of non-commuting Gibbs states and non-trivially entangled mixed states that are stabilizable despite the lack of an underlying commuting structure, albeit scalability to arbitrary system size remains in this case an open question.Comment: 44 pages, main results are improved, several proofs are more streamlined, application section is refine

Symmetrization for Quantum Networks: a continuous-time approach

In this paper we propose a continuous-time, dissipative Markov dynamics that asymptotically drives a network of n-dimensional quantum systems to the set of states that are invariant under the action of the subsystem permutation group. The Lindblad-type generator of the dynamics is built with two-body subsystem swap operators, thus satisfying locality constraints, and preserve symmetric observables. The potential use of the proposed generator in combination with local control and measurement actions is illustrated with two applications: the generation of a global pure state and the estimation of the network size.Comment: submitted to MTNS 201

Feedback control of quantum state reduction

Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability