238 research outputs found
On the generation of sequential unitary gates from continuous time Schrodinger equations driven by external fields
In all the various proposals for quantum computers, a common feature is that
the quantum circuits are expected to be made of cascades of unitary
transformations acting on the quantum states. A framework is proposed to
express these elementary quantum gates directly in terms of the control inputs
entering into the continuous time forced Schrodinger equation.Comment: 10 page
Dynamics over Signed Networks
A signed network is a network with each link associated with a positive or
negative sign. Models for nodes interacting over such signed networks, where
two different types of interactions take place along the positive and negative
links, respectively, arise from various biological, social, political, and
economic systems. As modifications to the conventional DeGroot dynamics for
positive links, two basic types of negative interactions along negative links,
namely the opposing rule and the repelling rule, have been proposed and studied
in the literature. This paper reviews a few fundamental convergence results for
such dynamics over deterministic or random signed networks under a unified
algebraic-graphical method. We show that a systematic tool of studying node
state evolution over signed networks can be obtained utilizing generalized
Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie
Discrete-Time Controllability for Feedback Quantum Dynamics
Controllability properties for discrete-time, Markovian quantum dynamics are
investigated. We find that, while in general the controlled system is not
finite-time controllable, feedback control allows for arbitrary asymptotic
state-to-state transitions. Under further assumption on the form of the
measurement, we show that finite-time controllability can be achieved in a time
that scales linearly with the dimension of the system, and we provide an
iterative procedure to design the unitary control actions
Sampling-based learning control of inhomogeneous quantum ensembles
Compensation for parameter dispersion is a significant challenge for control
of inhomogeneous quantum ensembles. In this paper, we present a systematic
methodology of sampling-based learning control (SLC) for simultaneously
steering the members of inhomogeneous quantum ensembles to the same desired
state. The SLC method is employed for optimal control of the state-to-state
transition probability for inhomogeneous quantum ensembles of spins as well as
type atomic systems. The procedure involves the steps of (i) training
and (ii) testing. In the training step, a generalized system is constructed by
sampling members according to the distribution of inhomogeneous parameters
drawn from the ensemble. A gradient flow based learning and optimization
algorithm is adopted to find the control for the generalized system. In the
process of testing, a number of additional ensemble members are randomly
selected to evaluate the control performance. Numerical results are presented
showing the success of the SLC method.Comment: 8 pages, 9 figure
Decompositions of Hilbert Spaces, Stability Analysis and Convergence Probabilities for Discrete-Time Quantum Dynamical Semigroups
We investigate convergence properties of discrete-time semigroup quantum
dynamics, including asymptotic stability, probability and speed of convergence
to pure states and subspaces. These properties are of interest in both the
analysis of uncontrolled evolutions and the engineering of controlled dynamics
for quantum information processing. Our results include two Hilbert space
decompositions that allow for deciding the stability of the subspace of
interest and for estimating of the speed of convergence, as well as a formula
to obtain the limit probability distribution for a set of orthogonal invariant
subspaces.Comment: 14 pages, no figures, to appear in Journal of Physics A, 201
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