  We review existing methods for implementing smooth functions f(A) of a sparse
Hermitian matrix A on a quantum computer, and analyse a further combination of
these techniques which has some advantages of simplicity and resource
consumption in some cases. Our construction uses the linear combination of
unitaries method with Chebyshev polynomial approximations. The query complexity
we obtain is O(log C/eps) where eps is the approximation precision, and C>0 is
an upper bound on the magnitudes of the derivatives of the function f over the
domain of interest. The success probability depends on the 1-norm of the Taylor
series coefficients of f, the sparsity d of the matrix, and inversely on the
smallest singular value of the target matrix f(A).
