A projected gradient method for optimization over density matrices

@article{Gonalves2016APG,
  title={A projected gradient method for optimization over density matrices},
  author={D. Gonçalves and M. A. Gomes-Ruggiero and C. Lavor},
  journal={Optimization Methods and Software},
  year={2016},
  volume={31},
  pages={328 - 341}
}
An ensemble of quantum states can be described by a Hermitian, positive semidefinite and unit trace matrix called density matrix. Thus, the study of methods for optimizing a certain function (energy, entropy) over the set of density matrices has a direct application to important problems in quantum information and computation. We propose a projected gradient method for solving such problems. By exploiting the geometry of the feasible set, which is the intersection of the cone of Hermitian… Expand
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