In this talk, we consider the problem of numerically computing (or approximating) the trace of a matrix function f(A). Important examples include the matrix logarithm, the entropy, and the exponential, which play key roles in quantum optimal transport formulations. We will present an overview of numerical linear algebra techniques to approximate such traces efficiently. In particular, we describe the Hutchinson trace estimator -- a stochastic algorithm that approximates the trace using quadratic forms involving the matrix and some random vectors -- and some variants including partial trace approximation and variance reduction techniques.
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