  Quantum algorithms for scientific computing require modules implementing
fundamental functions, such as the square root, the logarithm, and others. We
require algorithms that have a well-controlled numerical error, that are
uniformly scalable and reversible (unitary), and that can be implemented
efficiently. We present quantum algorithms and circuits for computing the
square root, the natural logarithm, and arbitrary fractional powers. We provide
performance guarantees in terms of their worst-case accuracy and cost. We
further illustrate their performance by providing tests comparing them to the
respective floating point implementations found in widely used numerical
software.
