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

Algorithm 950: Ncpol2sdpa---Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables