Abstract
The development of quantum computation has resulted in many quantum algorithms for a wide array of tasks. Recently, there is a growing interest in using quantum computing techniques to estimate or compute quantum information-theoretic quantities such as Renyi entropy, Von Neumann entropy, matrix means, etc. Motivated by these results, we present quantum algorithms for computing the maximal quantum -divergences and the operator-theoretic matrix Kubo--Ando means. Both of them involve Renyi entropies, matrix means as special cases, thus implying the universality of our framework.