Quantum circuits design for evaluating transcendental functions based on a function-value binary expansion method

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 using a novel methodology, which is called quantum function-value binary expansion (qFBE) method. This method transforms the evaluation of transcendental functions to the computation of algebraic functions, and output the binary solution digit-by-digit in a simple recursive way. The quantum circuits for solving the logarithmic, exponential, trigonometric and inverse trigonometric functions are presented 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 can be the essential building block for many quantum algorithms.