Quantum Optimal Transport: Regularization and Algorithms

Quantum Optimal Transport (QOT) extends optimal transport to quantum data such as states and channels. In this paper, we develop and benchmark computational algorithms for QOT, focusing on the quantum analog of the Sinkhorn algorithm~\cite{Cut13}. Applications include the QOT between quantum channels~\cite{DePTre-AnnHP-2021} and spin systems, where numerical tests show accurate and efficient performance. Our work bridges quantum information, convex optimization, and statistical physics, providing practical tools for quantum machine learning and machine learning for quantum data.