3,181 research outputs found
Robust quantum control by shaped pulse
Considering the problem of the control of a two-state quantum system by an
external field, we establish a general and versatile method that allows the
derivation of smooth pulses, suitable for ultrafast applications, that feature
the properties of high-fidelity, robustness, and low area. Such shaped pulses
can be viewed as a single-shot generalization of the composite pulse technique
with a time-dependent phase
Levelable Sets and the Algebraic Structure of Parameterizations
Asking which sets are fixed-parameter tractable for a given parameterization
constitutes much of the current research in parameterized complexity theory.
This approach faces some of the core difficulties in complexity theory. By
focussing instead on the parameterizations that make a given set
fixed-parameter tractable, we circumvent these difficulties. We isolate
parameterizations as independent measures of complexity and study their
underlying algebraic structure. Thus we are able to compare parameterizations,
which establishes a hierarchy of complexity that is much stronger than that
present in typical parameterized algorithms races. Among other results, we find
that no practically fixed-parameter tractable sets have optimal
parameterizations
Statistical and Computational Tradeoffs in Stochastic Composite Likelihood
Maximum likelihood estimators are often of limited practical use due to the
intensive computation they require. We propose a family of alternative
estimators that maximize a stochastic variation of the composite likelihood
function. Each of the estimators resolve the computation-accuracy tradeoff
differently, and taken together they span a continuous spectrum of
computation-accuracy tradeoff resolutions. We prove the consistency of the
estimators, provide formulas for their asymptotic variance, statistical
robustness, and computational complexity. We discuss experimental results in
the context of Boltzmann machines and conditional random fields. The
theoretical and experimental studies demonstrate the effectiveness of the
estimators when the computational resources are insufficient. They also
demonstrate that in some cases reduced computational complexity is associated
with robustness thereby increasing statistical accuracy.Comment: 30 pages, 97 figures, 2 author
A Robust Semidefinite Programming Approach to the Separability Problem
We express the optimization of entanglement witnesses for arbitrary bipartite
states in terms of a class of convex optimization problems known as Robust
Semidefinite Programs (RSDP). We propose, using well known properties of RSDP,
several new sufficient tests for the separability of mixed states. Our results
are then generalized to multipartite density operators.Comment: Revised version (minor spell corrections) . 6 pages; submitted to
Physical Review
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