  Quantum arithmetic in the computational basis constitutes the fundamental
component of many circuit-based quantum algorithms. There exist a lot of
studies about reversible implementations of algebraic functions, while research
on the higher-level transcendental functions is scant. We propose to evaluate
the transcendental functions based on a novel methodology, which is called qFBE
(quantum Function-value Binary Expansion) method. This method transforms the
evaluation of transcendental functions to the computation of algebraic
functions in a simple recursive way. We present the quantum circuits for
solving the logarithmic, exponential, trigonometric and inverse trigonometric
functions based on the qFBE method. The efficiency of the circuits is
demonstrated on a quantum virtual computing system installed on the Sunway
TaihuLight supercomputer. The qFBE method provides a unified and programmed
solution for the evaluation of transcendental functions, and it will be an
important building block for many quantum algorithms.
