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

TL;DR

This paper introduces the qFBE method, a novel quantum circuit design that efficiently evaluates transcendental functions by transforming them into algebraic functions, facilitating their use in quantum algorithms.

Contribution

The paper presents a new recursive qFBE methodology and corresponding quantum circuits for transcendental functions, filling a research gap in higher-level quantum arithmetic.

Findings

Quantum circuits for logarithmic, exponential, and trigonometric functions demonstrated.

Efficiency validated on a supercomputer-based quantum virtual system.

Provides a unified approach for transcendental function evaluation in quantum computing.

Abstract

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.