Maximizing concave piecewise affine functions on the unitary group
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We show that a convex relaxation, introduced by Sridharan, McEneaney, Gu and James to approximate the value function of an optimal control problem arising from quantum gate synthesis, is exact. This relaxation applies to the maximization of a class of concave piecewise affine functions over the unitary group.
KeywordsConvex relaxation Unitary group Optimal control Quantum control Approximate dynamic programming
Z. Qu carried out parts of this work when she was with INRIA and CMAP, École Polytechnique, CNRS and subsequently with the School of Mathematics of University of Edinburgh. S. Sridharan carried out part of this work when he was with UMA, ENSTA, Palaiseau, France. S. Gaubert and Z. Qu were partially supported by the PGMO Program of FMJH and EDF, and by the program “Ingénierie Numérique & Sécurité” of the French National Agency of Research, Project “MALTHY”, Number ANR-13-INSE-0003.
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