Algorithm 950: Ncpol2sdpa -- sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables. 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 variables 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 such as finding the ground state energy or testing quantum correlations.
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References in zbMATH (referenced in 3 articles , 1 standard article )
Showing results 1 to 3 of 3.
- Kussaba, Hugo T. M.; Ishihara, João Y.; Menezes, Leonardo R. A. X.: A robust unscented transformation for uncertain moments (2019)
- Curchod, Florian J.; Johansson, Markus; Augusiak, Remigiusz; Hoban, Matty J.; Wittek, Peter; Acín, Antonio: A single entangled system is an unbounded source of nonlocal correlations and of certified random numbers (2018)
- Wittek, Peter: Algorithm 950: Ncpol2sdpa -- sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables (2015)