Quantum circuits design for evaluating transcendental functions based on a function-value binary expansion method
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Quantum circuits design for evaluating transcendental functions based on a function-value binary expansion method Shengbin Wang1 · Zhimin Wang1 · Wendong Li1 · Lixin Fan1 · Guolong Cui1 · Zhiqiang Wei2 · Yongjian Gu1 Received: 26 February 2020 / Accepted: 1 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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 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. Keywords Quantum circuit · Quantum arithmetic · Algebraic function · Transcendental function · Function-value binary expansion
Shengbin Wang and Zhimin Wang have contributed equally to this work. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11128-02 0-02855-7) contains supplementary material, which is available to authorized users.
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Zhimin Wang [email protected] Yongjian Gu [email protected]
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Department of Physics, College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China
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Department of Computer Science and Technology, College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China 0123456789().: V,-vol
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1 Introduction After decades of efforts, people are beginning to realize the promise of quantum computing that quantum computers have capabilities surpassing what classical computers can do [1, 2]. Quantum speedup is typically considered as the asymptotic scaling of complexity measures of quantum algorithm with problem size [3]. Now from an implementation-of-algorithm point of view, ongoing work is desired to provide more detailed cost estimates and practicality analysis of various quantum algorithms. To do this, quantum arithmetic would be the always-encountered obstacle, which is always treated as oracles in quantum algorithm because it has no influence on measuring the asymptotic complexity. Arithmetic in the computational basis constitutes the fundamental component of many circuit-based quantum algorithms. The most famous example is
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