Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck

TL;DR

This paper extends the quantum Arimoto-Blahut algorithm to handle linear constraints on density matrices, enabling broader quantum optimization applications, and demonstrates its effectiveness in quantum information bottleneck tasks compared to previous methods.

Contribution

The paper introduces a generalized quantum Arimoto-Blahut algorithm applicable to constrained quantum optimization problems, expanding its utility in quantum information processing.

Findings

The generalized algorithm applies to a wider class of quantum optimization problems.

Numerical results show improved performance over previous algorithms.

The method is effective for quantum learning tasks involving the information bottleneck.

Abstract

We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al. (IEEE Trans. IT, 67, 946 (2021)) to a function defined over a set of density matrices with linear constraints so that our algorithm can be applied to optimizations of quantum operations. This algorithm has wider applicability. Hence, we apply our algorithm to the quantum information bottleneck with three quantum systems, which can be used for quantum learning. We numerically compare our obtained algorithm with the existing algorithm by Grimsmo and Still (Phys. Rev. A, 94, 012338 (2016)). Our numerical analysis shows that our algorithm is better than their algorithm.