Quantum information bottleneck was proposed by Grimsmo and Still (2016 Phys. Rev. A 94 012338) as a promising method for quantum supervised machine learning. To study this method, we generalize the quantum Arimoto–Blahut algorithm by Ramakrishnan et al (2021 IEEE Trans. Inf. Theory 67 946) 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, and we apply our algorithm to the quantum information bottleneck with three quantum systems. We numerically compare our obtained algorithm with the existing algorithm by Grimsmo and Still. Our numerical analysis shows that our algorithm is better than their algorithm.

中文翻译：

---

广义量子Arimoto-Blahut算法及其在量子信息瓶颈中的应用


量子信息瓶颈由 Grimsmo 和 Still (2016 Phys. Rev. A 94 012338) 提出，作为量子监督机器学习的一种有前景的方法。为了研究这种方法，我们将 Ramakrishnan 等人 (2021 IEEE Trans. Inf. Theory67 946) 的量子 Arimoto-Blahut 算法推广为在一组具有线性约束的密度矩阵上定义的函数，以便我们的算法可以应用于优化量子运算。该算法具有更广泛的适用性，我们将我们的算法应用于具有三个量子系统的量子信息瓶颈。我们将我们获得的算法与 Grimsmo 和 Still 的现有算法进行数值比较。我们的数值分析表明我们的算法比他们的算法更好。