A LONE code for the sparse control of quantum systems

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• 作者：G. Ciaramella^a ; A. Borzì ; ^b ; ^{alfio.borzi@mathematik.uni-wuerzburg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quantum spin systems ; Liouville&ndash ; von Neumann master equation ; Schrö ; dinger equation ; Nonsmooth optimization ; Optimal control theory ; Sparsity ; Semi-smooth Newton scheme
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：200
• 期：Complete
• 页码：312-323
• 全文大小：492 K

文摘

In 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$L^1$-penalized cost functionals. In this paper, the MATLAB package LONE is presented aimed to solving L¹$L^1$-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-$\frac{1}{2}$ sparse optimal control problems.

Solution method: Full-complex semi-smooth Newton method and continuation techniques

Running time: 60–600 sec