  Efficiently processing basic linear algebra subroutines is of great
importance for a wide range of computational problems. In this paper, we
consider techniques to implement matrix functions on a quantum computer, which
are composed of basic matrix operations on a set of matrices. These matrix
operations include addition, multiplication, Kronecker sum, tensor product,
Hadamard product, and single-matrix functions. We discuss the composed matrix
functions in terms of the estimation of scalar quantities such as inner
products, trace, determinant and Schatten p-norms. We thus provide a framework
for compiling instructions for linear algebraic computations into gate
sequences on actual quantum computers.
