こんな論文が発表されていた。今、どこかで査読中だと思います。github 使ってソフトウェアも公開中です。
Ncpol2sdpa -- Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
Peter Wittek
(Submitted on 28 Aug 2013)
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 resulting relaxation. Constrained problems with a relaxation of order two may contain up to a hundred variables. The implementation is available in C++ and Python. The tool helps solve problems such as finding the ground state energy or testing quantum correlations.
Ncpol2sdpa -- Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
Peter Wittek
(Submitted on 28 Aug 2013)
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 resulting relaxation. Constrained problems with a relaxation of order two may contain up to a hundred variables. The implementation is available in C++ and Python. The tool helps solve problems such as finding the ground state energy or testing quantum correlations.
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