1,277 research outputs found
Critical points of the optimal quantum control landscape: a propagator approach
Numerical and experimental realizations of quantum control are closely
connected to the properties of the mapping from the control to the unitary
propagator. For bilinear quantum control problems, no general results are
available to fully determine when this mapping is singular or not. In this
paper we give suffcient conditions, in terms of elements of the evolution
semigroup, for a trajectory to be non-singular. We identify two lists of
"way-points" that, when reached, ensure the non-singularity of the control
trajectory. It is found that under appropriate hypotheses one of those lists
does not depend on the values of the coupling operator matrix
Singularity-free quantum tracking control of molecular rotor orientation
Quantum tracking control aims to identify applied fields to steer the
expectation values of particular observables along desired paths in time. The
associated temporal fields can be identified by inverting the underlying
dynamical equations for the observables. However, fields found in this manner
are often plagued by undesirable singularities. In this paper we consider a
planar molecular rotor, and derive singularity-free tracking expressions for
the fields that steer the expectation of the orientation of the rotor along
desired trajectories in time. Simulations are presented that utilize two
orthogonal control electric fields to drive the orientation of the rotor along
a series of designated tracks
Characterization of the Critical Sets of Quantum Unitary Control Landscapes
This work considers various families of quantum control landscapes (i.e.
objective functions for optimal control) for obtaining target unitary
transformations as the general solution of the controlled Schr\"odinger
equation. We examine the critical point structure of the kinematic landscapes
J_F (U) = ||(U-W)A||^2 and J_P (U) = ||A||^4 - |Tr(AA'W'U)|^2 defined on the
unitary group U(H) of a finite-dimensional Hilbert space H. The parameter
operator A in B(H) is allowed to be completely arbitrary, yielding an objective
function that measures the difference in the actions of U and the target W on a
subspace of state space, namely the column space of A. The analysis of this
function includes a description of the structure of the critical sets of these
kinematic landscapes and characterization of the critical points as maxima,
minima, and saddles. In addition, we consider the question of whether these
landscapes are Morse-Bott functions on U(H). Landscapes based on the intrinsic
(geodesic) distance on U(H) and the projective unitary group PU(H) are also
considered. These results are then used to deduce properties of the critical
set of the corresponding dynamical landscapes.Comment: 15 pages, 3 figure
Exploring Quantum Control Landscape Structure
A common goal of quantum control is to maximize a physical observable through
the application of a tailored field. The observable value as a function of the
field constitutes a quantum control landscape. Previous works have shown, under
specified conditions, that the quantum control landscape should be free of
suboptimal critical points. This favorable landscape topology is one factor
contributing to the efficiency of climbing the landscape. An additional,
complementary factor is the landscape \textit{structure}, which constitutes all
non-topological features. If the landscape's structure is too complex, then
climbs may be forced to take inefficient convoluted routes to finding optimal
controls. This paper provides a foundation for understanding control landscape
structure by examining the linearity of gradient-based optimization
trajectories through the space of control fields. For this assessment, a metric
is defined as the ratio of the path length of the optimization
trajectory to the Euclidean distance between the initial control field and the
resultant optimal control field that takes an observable from the bottom to the
top of the landscape. Computational analyses for simple model quantum systems
are performed to ascertain the relative abundance of nearly straight control
trajectories encountered when optimizing a state-to-state transition
probability. The collected results indicate that quantum control landscapes
have very simple structural features. The favorable topology and the
complementary simple structure of the control landscape provide a basis for
understanding the generally observed ease of optimizing a state-to-state
transition probability.Comment: 27 pages, 7 figure
An Analysis of Traditional Issue Specific and Macroeconomic Variables on US Commercial Mortgage Backed Securities
This paper examines the effects of traditional issue-specific commercial mortgage backed securities (CMBS) variables on US CMBS spreads. In addition, a decomposition of the Conference Board?s US Leading Economic Indicators (LEI) Index will be examined for each of the ten component?s explanatory power for US CMBS spreads. A qualitative examination of the history and setting of the US subprime crisis, features of US CMBS, and an outline of The Conference Board?s US LEI components are provided. This is followed by an explanation of assumptions and the methodology used for the statistical analysis of the fourteen variables on CMBS spreads. In addition, the NA REIT Composite Index Dividend Yield is hypothesized to contribute to the CMBS spreads. A conclusion will contain results and proposals for an improved model, in contrast to Jadeja and Dorokov (Summer 2008). This paper closes with a discussion of possible sources of errors and guidance for future studies
Exploration of the memory effect on the photon-assisted tunneling via a single quantum dot: A generalized Floquet theoretical approach
The generalized Floquet approach is developed to study memory effect on
electron transport phenomena through a periodically driven single quantum dot
in an electrode-multi-level dot-electrode nanoscale quantum device. The memory
effect is treated using a multi-function Lorentzian spectral density (LSD)
model that mimics the spectral density of each electrode in terms of multiple
Lorentzian functions. For the symmetric single-function LSD model involving a
single-level dot, the underlying single-particle propagator is shown to be
related to a 2 x 2 effective time-dependent Hamiltonian that includes both the
periodic external field and the electrode memory effect. By invoking the
generalized Van Vleck (GVV) nearly degenerate perturbation theory, an
analytical Tien-Gordon-like expression is derived for arbitrary order multi-
photon resonance d.c. tunneling current. Numerically converged simulations and
the GVV analytical results are in good agreement, revealing the origin of
multi- photon coherent destruction of tunneling and accounting for the
suppression of the staircase jumps of d.c. current due to the memory effect.
Specially, a novel blockade phenomenon is observed, showing distinctive
oscillations in the field-induced current in the large bias voltage limit
Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window
The past decade has witnessed many interesting algorithms for maintaining
statistics over a data stream. This paper initiates a theoretical study of
algorithms for monitoring distributed data streams over a time-based sliding
window (which contains a variable number of items and possibly out-of-order
items). The concern is how to minimize the communication between individual
streams and the root, while allowing the root, at any time, to be able to
report the global statistics of all streams within a given error bound. This
paper presents communication-efficient algorithms for three classical
statistics, namely, basic counting, frequent items and quantiles. The
worst-case communication cost over a window is bits for basic counting and words for the remainings, where is the number of distributed
data streams, is the total number of items in the streams that arrive or
expire in the window, and is the desired error bound. Matching
and nearly matching lower bounds are also obtained.Comment: 12 pages, to appear in the 27th International Symposium on
Theoretical Aspects of Computer Science (STACS), 201
DeepStory: Video Story QA by Deep Embedded Memory Networks
Question-answering (QA) on video contents is a significant challenge for
achieving human-level intelligence as it involves both vision and language in
real-world settings. Here we demonstrate the possibility of an AI agent
performing video story QA by learning from a large amount of cartoon videos. We
develop a video-story learning model, i.e. Deep Embedded Memory Networks
(DEMN), to reconstruct stories from a joint scene-dialogue video stream using a
latent embedding space of observed data. The video stories are stored in a
long-term memory component. For a given question, an LSTM-based attention model
uses the long-term memory to recall the best question-story-answer triplet by
focusing on specific words containing key information. We trained the DEMN on a
novel QA dataset of children's cartoon video series, Pororo. The dataset
contains 16,066 scene-dialogue pairs of 20.5-hour videos, 27,328 fine-grained
sentences for scene description, and 8,913 story-related QA pairs. Our
experimental results show that the DEMN outperforms other QA models. This is
mainly due to 1) the reconstruction of video stories in a scene-dialogue
combined form that utilize the latent embedding and 2) attention. DEMN also
achieved state-of-the-art results on the MovieQA benchmark.Comment: 7 pages, accepted for IJCAI 201
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