8,476 research outputs found
Stabilizing feedback controls for quantum systems
No quantum measurement can give full information on the state of a quantum
system; hence any quantum feedback control problem is neccessarily one with
partial observations, and can generally be converted into a completely observed
control problem for an appropriate quantum filter as in classical stochastic
control theory. Here we study the properties of controlled quantum filtering
equations as classical stochastic differential equations. We then develop
methods, using a combination of geometric control and classical probabilistic
techniques, for global feedback stabilization of a class of quantum filters
around a particular eigenstate of the measurement operator
Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition
We analyze the asymptotic behavior of discrete-time, Markovian quantum
systems with respect to a subspace of interest. Global asymptotic stability of
subspaces is relevant to quantum information processing, in particular for
initializing the system in pure states or subspace codes. We provide a
linear-algebraic characterization of the dynamical properties leading to
invariance and attractivity of a given quantum subspace. We then construct a
design algorithm for discrete-time feedback control that allows to stabilize a
target subspace, proving that if the control problem is feasible, then the
algorithm returns an effective control choice. In order to prove this result, a
canonical QR matrix decomposition is derived, and also used to establish the
control scheme potential for the simulation of open-system dynamics.Comment: 12 pages, 1 figur
Quantum control theory and applications: A survey
This paper presents a survey on quantum control theory and applications from
a control systems perspective. Some of the basic concepts and main developments
(including open-loop control and closed-loop control) in quantum control theory
are reviewed. In the area of open-loop quantum control, the paper surveys the
notion of controllability for quantum systems and presents several control
design strategies including optimal control, Lyapunov-based methodologies,
variable structure control and quantum incoherent control. In the area of
closed-loop quantum control, the paper reviews closed-loop learning control and
several important issues related to quantum feedback control including quantum
filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective,
some references are added, published versio
Asymptotic ensemble stabilizability of the Bloch equation
In this paper we are concerned with the stabilizability to an equilibrium
point of an ensemble of non interacting half-spins. We assume that the spins
are immersed in a static magnetic field, with dispersion in the Larmor
frequency, and are controlled by a time varying transverse field. Our goal is
to steer the whole ensemble to the uniform "down" position. Two cases are
addressed: for a finite ensemble of spins, we provide a control function (in
feedback form) that asymptotically stabilizes the ensemble in the "down"
position, generically with respect to the initial condition. For an ensemble
containing a countable number of spins, we construct a sequence of control
functions such that the sequence of the corresponding solutions pointwise
converges, asymptotically in time, to the target state, generically with
respect to the initial conditions. The control functions proposed are uniformly
bounded and continuous
- …