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arXiv 2001.00807quant-ph
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基于函数值二进制展开法的超越函数量子线路设计

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

Shengbin Wang, Zhimin Wang, Wendong Li, Lixin Fan, Guolong Cui, Zhiqiang Wei, Yongjian Gu

摘要:

计算基础中的量子算术构成了许多基于电路的量子算法的基本组成部分。关于代数函数的可逆实现的研究很多,而对于更高层次的超越函数的研究却很少。我们提出了一种新的方法,这是所谓的qFBE(量子函数值二进制扩展)方法的基础上评估的超越函数。该方法以简单的递归方式将超越函数的计算转化为代数函数的计算。基于qFBE方法,我们给出了求解对数、指数、三角和反三角函数的量子线路。电路的效率在安装在Sunway TaihuLight超级计算机上的量子虚拟计算系统上得到了证明。qFBE方法为超越函数的计算提供了一个统一的程序化解决方案,它将成为许多量子算法的重要组成部分。

英文摘要:

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.

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