Fixed Parameter Algorithms and Hardness of Approximation Results for the Structural Target Controllability Problem

2018 ◽  
pp. 103-114
Author(s):  
Eugen Czeizler ◽  
Alexandru Popa ◽  
Victor Popescu
Keyword(s):  
Hardness Of Approximation ◽  
Controllability Problem ◽  
Fixed Parameter

scholarly journals Fixed-Parameter Extrapolation and Aperiodic Order

2018 ◽  
Vol 49 (3) ◽  
pp. 35-47
Author(s):  
Stephen Fenner ◽  
Frederic Green ◽  
Steven Homer
Keyword(s):  
Aperiodic Order ◽  
Fixed Parameter

The complexity of fixed-parameter problems

2008 ◽  
Vol 39 (1) ◽  
pp. 33-46 ◽  
Author(s):  
Jonathan F. Buss ◽  
Tarique M. Islam
Keyword(s):  
Fixed Parameter

scholarly journals Eisenstein series and an asymptotic for the K-Bessel function

2021 ◽  
Author(s):  
Jimmy Tseng
Keyword(s):  
Asymptotic Expansion ◽  
Bessel Function ◽  
Eisenstein Series ◽  
Uniform Estimate ◽  
Positive Real ◽  
Dominant Term ◽  
Complex Order ◽  
Fixed Parameter ◽  
Real Argument ◽  
Real Analytic

AbstractWe produce an estimate for the K-Bessel function $$K_{r + i t}(y)$$ K r + i t ( y ) with positive, real argument y and of large complex order $$r+it$$ r + i t where r is bounded and $$t = y \sin \theta $$ t = y sin θ for a fixed parameter $$0\le \theta \le \pi /2$$ 0 ≤ θ ≤ π / 2 or $$t= y \cosh \mu $$ t = y cosh μ for a fixed parameter $$\mu >0$$ μ > 0 . In particular, we compute the dominant term of the asymptotic expansion of $$K_{r + i t}(y)$$ K r + i t ( y ) as $$y \rightarrow \infty $$ y → ∞ . When t and y are close (or equal), we also give a uniform estimate. As an application of these estimates, we give bounds on the weight-zero (real-analytic) Eisenstein series $$E_0^{(j)}(z, r+it)$$ E 0 ( j ) ( z , r + i t ) for each inequivalent cusp $$\kappa _j$$ κ j when $$1/2 \le r \le 3/2$$ 1 / 2 ≤ r ≤ 3 / 2 .

scholarly journals Fixed-Parameter Algorithms for Unsplittable Flow Cover

2021 ◽  
Author(s):  
Andrés Cristi ◽  
Mathieu Mari ◽  
Andreas Wiese
Keyword(s):  
Fixed Parameter ◽  
Unsplittable Flow

scholarly journals Fixed-parameter tractability and lower bounds for stabbing problems

2013 ◽  
Vol 46 (7) ◽  
pp. 839-860 ◽  
Author(s):  
Panos Giannopoulos ◽  
Christian Knauer ◽  
Günter Rote ◽  
Daniel Werner
Keyword(s):  
Lower Bounds ◽  
Fixed Parameter Tractability ◽  
Fixed Parameter

On the complexity of fixed parameter problems

1989 ◽  
Author(s):  
K.R. Abrahamson ◽  
M.R. Fellows ◽  
J.A. Ellis ◽  
M.E. Mata
Keyword(s):  
Fixed Parameter

scholarly journals The robust minimal controllability problem

Automatica ◽  
2017 ◽  
Vol 82 ◽  
pp. 261-268 ◽  
Author(s):  
Sérgio Pequito ◽  
Guilherme Ramos ◽  
Soummya Kar ◽  
A. Pedro Aguiar ◽  
Jaime Ramos
Keyword(s):  
Controllability Problem

scholarly journals Transforming graph states using single-qubit operations

2018 ◽  
Vol 376 (2123) ◽  
pp. 20170325 ◽  
Author(s):  
Axel Dahlberg ◽  
Stephanie Wehner
Keyword(s):  
Quantum Information ◽  
Error Correcting Codes ◽  
Graph States ◽  
Target State ◽  
Single Qubit ◽  
Minor Problem ◽  
Fixed Parameter ◽  
Source State ◽  
Quantum Error ◽  
Stabilizer States

Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from another stabilizer (source) state by single-qubit Clifford operations (LC), single-qubit Pauli measurements (LPM) and classical communication (CC) between sites holding the individual qubits. What is more, we provide a recipe to obtain the sequence of LC+LPM+CC operations which prepare the desired target state from the source state, and show how these operations can be applied in parallel to reach the target state in constant time. Our algorithm has applications in quantum networks, quantum computing, and can also serve as a design tool—for example, to find transformations between quantum error correcting codes. We provide a software implementation of our algorithm that makes this tool easier to apply. A key insight leading to our algorithm is to show that the problem is equivalent to one in graph theory, which is to decide whether some graph G ′ is a vertex-minor of another graph G . The vertex-minor problem is, in general, -Complete, but can be solved efficiently on graphs which are not too complex. A measure of the complexity of a graph is the rank-width which equals the Schmidt-rank width of a subclass of stabilizer states called graph states, and thus intuitively is a measure of entanglement. Here, we show that the vertex-minor problem can be solved in time O (| G | 3 ), where | G | is the size of the graph G , whenever the rank-width of G and the size of G ′ are bounded. Our algorithm is based on techniques by Courcelle for solving fixed parameter tractable problems, where here the relevant fixed parameter is the rank width. The second half of this paper serves as an accessible but far from exhausting introduction to these concepts, that could be useful for many other problems in quantum information. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

Sign in / Sign up

Export Citation Format

Share Document