  A majority of numerical scientific computation relies heavily on handling and
manipulating matrices, such as solving linear equations, finding eigenvalues
and eigenvectors, and so on. Many quantum algorithms have been developed to
advance these computational tasks, and in some cases, such as solving linear
equations, can be shown to yield exponential speedup. Here, employing the
techniques in the HHL algorithm and the ideas of the classical power method, we
provide a simple quantum algorithm for estimating the largest eigenvalue in
magnitude of a given Hermitian matrix. As in the case of the HHL algorithm, our
quantum procedure can also yield exponential speedup compared to classical
algorithms that solve the same problem. We also discuss a few possible
extensions and applications of our quantum algorithm, such as a version of a
hybrid quantum-classical Lanczos algorithm.
