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Ncpol2sdpa – Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
University of Borås, Faculty of Librarianship, Information, Education and IT.ORCID iD: 0000-0002-1539-8256
2015 (English)In: ACM Transactions on Mathematical Software, ISSN 0098-3500, E-ISSN 1557-7295, Vol. 41, no 3Article in journal (Refereed) PublishedText
Abstract [en]

A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only problems of commuting variables have efficient generators. We develop an implementation for problems of noncommuting problems that creates the relaxation to be solved by SDPA -- a high-performance solver that runs in a distributed environment. We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of the resulting relaxations. Constrained problems with a relaxation of order two may contain up to a hundred variables. The implementation is available in Python. The tool helps solve problems such as finding the ground state energy or testing quantum correlations.

Place, publisher, year, edition, pages
2015. Vol. 41, no 3
Keyword [en]
semidefinite programming, SDP, polynomial optimization problem, noncommuting variables, Python, C++, symbolic calculation
National Category
Computational Mathematics
Research subject
Library and Information Science
URN: urn:nbn:se:hb:diva-8543DOI: 10.1145/2699464OAI: diva2:894328
Available from: 2016-01-14 Created: 2016-01-14 Last updated: 2016-02-15Bibliographically approved

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