Interpolation of positive matrices by quantum‐inspired optimal control

Abstract

AbstractInterpolation of probability distributions can be formulated as an optimal transport problem. Positive matrix, which can be viewed as the generalization of probability distribution to higher dimension, is used in quantum theory to describe the state of a quantum system. Here, a quantum‐inspired method for the interpolation of positive matrices is proposed. Particularly, this method employs the quantum state purification of the positive matrices in an extended space. Since pure state controllability can be easily achieved using open‐loop coherent control, the continuous interpolation of positive matrices is given as a completely positive map induced by simulating the optimal control for pure state transfer. The quantum‐inspired interpolation is shape‐preserving with applications to tensor field processing.