1,721,019 research outputs found
-norm exact control of the Pauli equation
No full textA computational framework for the exact-control of the magnetic state and the spin of an electron is presented. The evolution of this quantum system is governed by the Pauli equation, that is a system of Schrodinger equations coupled by the action of magnetic fields. The magnetic fields are used as controls in order to steer the quantum system from an initial state to a desired target state at a given final time. This control framework is based on a minimum norm optimization formulation of exact-controllability quantum problems, that allows the application of efficient Krylov-Newton optimization techniques. In order to provide this framework with an adequate initialization, a continuation procedure is discussed. Results of numerical experiments demonstrate the effectiveness of the proposed framework
SKRYN: A fast semismooth-Krylov-Newton method for controlling Ising spin systems
No full textThe modeling and control of Ising spin systems is of fundamental importance in NMR spectroscopy applications. In this paper, two computer packages, ReHaG and SKRYN, are presented. Their purpose is to set-up and solve quantum optimal control problems governed by the Liouville master equation modeling Ising spin-12 systems with pointwise control constraints. In particular, the MATLAB package ReHaG allows to compute a real matrix representation of the master equation. The MATLAB package SKRYN implements a new strategy resulting in a globalized semismooth matrix-free Krylov-Newton scheme. To discretize the real representation of the Liouville master equation, a norm-preserving modified Crank-Nicolson scheme is used. Results of numerical experiments demonstrate that the SKRYN code is able to provide fast and accurate solutions to the Ising spin quantum optimization problem
A LONE code for the sparse control of quantum systems
No full textIn many applications with quantum spin systems, control functions with a sparse and pulse-shaped structure are often required. These controls can be obtained by solving quantum optimal control problems with L1-penalized cost functionals. In this paper, the MATLAB package LONE is presented aimed to solving L1-penalized optimal control problems governed by unitary-operator quantum spin models. This package implements a new strategy that includes a globalized semi-smooth Krylov-Newton scheme and a continuation procedure. Results of numerical experiments demonstrate the ability of the LONE code in computing accurate sparse optimal control solutions. Program summary Program title: LONE Catalogue identifier: AEYV-v1-0 Program summary URL:http://cpc.cs.qub.ac.UK/summaries/AEYV-v1-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.UK/licence/licence.html No. of lines in distributed program, including test data, etc.: 1683 No. of bytes in distributed program, including test data, etc.: 8654 Distribution format: tar.gz Programming language: MATLAB - (OCTAVE). Computer: Any capable of running MATLAB or OCTAVE. Operating system: Any capable of running MATLAB or OCTAVE. RAM: Bytes Classification: 4.9. External routines: gmres MATLAB routine Nature of problem: A semi-smooth Newton scheme for solving quantum spin-12 sparse optimal control problems. Solution method: Full-complex semi-smooth Newton method and continuation techniques Running time: 60-600 sec
Quantum Optimal Control Problems with a Sparsity Cost Functional
No full textIn this article, the investigation of a class of quantum optimal control problems with L1 sparsity cost functionals is presented. The focus is on quantum systems modeled by Schrödinger-type equations with a bilinear control structure as it appears in many applications in nuclear magnetic resonance spectroscopy, quantum imaging, quantum computing, and in chemical and photochemical processes. In these problems, the choice of L1 control spaces promotes sparse optimal control functions that are conveniently produced by laboratory pulse shapers. The characterization of L1 quantum optimal controls and an efficient numerical semi-smooth Newton solution procedure are discussed
Happy 25th Anniversary DDM! ... But How Fast Can the Schwarz Method Solve Your Logo?
No full text“Vous n’avez vraiment rien à faire”!1 This was the smiling reaction of Laurence Halpern when the first author told her about our wish to accurately estimate the convergence rate of the Schwarz method for the solution of the ddm logo2, see Figure 1 (left)
Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for time-periodic parabolic optimal control problems
No full textThis paper is concerned with a novel convergence analysis of the optimized Schwarz waveform relaxation method (OSWRM) for the solution of optimal control problems governed by periodic parabolic partial differential equations (PDEs). The new analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition. This leads to a precise characterization of the convergence factor of the method at the semidiscrete level. Using this characterization, the optimal transmission condition parameter is obtained at the semidiscrete level and its asymptotic behavior as the time discretization converges to zero is analyzed in detail
Unmapped Tent Pitching Schemes by Waveform Relaxation
No full textThe mapped tent pitching algorithm (MTP) is a very advanced domain decomposition strategy for the parallel solution of hyperbolic problems
R.E. property meets technology: cross-country comparison and general framework
Full text linkPurpose: Due to the young age of proptech, little is known about the dynamics of its expansion. In particular, there is limited agreement about a definition of “proptech,” while different categorizations are popping up. A severe lack of information emerges for the proptech scenario in Italy. The goal of this paper is to systematize multiple proptech maps in the attempt to create a framework for comparison of country-specific trends and an overarching definition of proptech. The research examines the evolutionary stage of the Italian digital real estate sector and compares it to the international context. Design/methodology/approach: An in-depth analysis of 12 proptech maps at both national and international level was conducted based on online research. A list of Italian proptech companies was composed through multiple methods. A map was built for a cross-country comparison. Findings: Each country or organization tends to develop its own categorization. This creates a multifaceted context where comparison and analysis are challenging. The Italian proptech sector seems underdeveloped compared to neighboring countries. Big room for improving the proptech business in this country still exists. Practical implications: The results are valuable for proptech start-ups, business investors and well-established real estate actors to build on new entrepreneurial initiatives. The opportunity to advance proptech mapping and categorization emerges as a prospect for future research. Originality/value: This research adds an overview of cross-country proptech categories and proposes the first analysis of Italian proptech. This will contribute to support entrepreneurial opportunities
A Nonlinear Optimized Schwarz Preconditioner for Elliptic Optimal Control Problems
No full textIn this section, we introduce an optimized Schwarz method (OSM) for solving the optimality system (3)
On the Scalability of the Parallel Schwarz Method in One-Dimension
No full textAn algorithm is said to beweakly scalable if it can solve progressively larger problems with an increasing number of processors in a fixed amount of time. According to classical Schwarz theory, the parallel Schwarz method (PSM) is not scalable (see, e.g., [2, 7])
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