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arXiv 2201.10574quant-phcs.CC
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基础量子算法

Basic Quantum Algorithms

National Laboratory of Scientific Computing（国家科学计算实验室）；LNCC/MCTI（国家科学计算实验室/巴西科学技术创新部）

Renato Portugal

备注：
170 pages
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AI总结：

本文回顾了早期量子算法的发展，包括Deutsch、Deutsch-Jozsa、Bernstein-Vazirani、Simon、Shor、Kitaev、Grover和HHL算法，分析了它们的核心方法和贡献。

摘要：

量子计算发展迅速，迫使我们重新审视和更新理论基础。《基础量子算法》回顾了最早的量子算法。旅程始于1985年，Deutsch尝试同时评估函数在两个域点的值。1992年，Deutsch和Jozsa创建了一个确定布尔函数是否恒定或平衡的量子算法。次年，Bernstein和Vazirani证明几乎相同的算法可用于识别特定布尔函数。1994年，Simon提出一个新型量子算法，以指数速度确定函数是一对一还是二对一。同年，Shor开发了两个突破性的量子算法，用于整数分解和离散对数计算，对广泛使用的密码方法构成威胁。1995年，Kitaev提出基于相位估计的替代方法，在多个应用中证明有价值。次年，Grover设计了一个比经典算法快平方根倍的量子搜索算法。十多年后，Harrow、Hassidim和Lloyd提出了用于求解线性方程组的量子算法，即HHL算法。本文重点在于电路模型，对这些杰出算法进行了详细描述。

英文摘要：

Quantum computing is evolving so rapidly that it forces us to revisit, rewrite, and update the foundations of the theory. \emph{Basic Quantum Algorithms} revisits the earliest quantum algorithms. The journey began in 1985 with Deutsch attempting to evaluate a function at two domain points simultaneously. Then, in 1992, Deutsch and Jozsa created a quantum algorithm that determines whether a Boolean function is constant or balanced. The following year, Bernstein and Vazirani realized that essentially the same algorithm could be used to identify a specific Boolean function within a set of linear Boolean functions. In 1994, Simon introduced a novel quantum algorithm that determines whether a function is one-to-one or two-to-one exponentially faster than any classical algorithm for the same problem. That same year, Shor developed two groundbreaking quantum algorithms for integer factoring and calculating discrete logarithms, posing a threat to widely used cryptographic methods. In 1995, Kitaev proposed an alternative formulation based on phase estimation that proved valuable in numerous applications. The following year, Grover devised a quantum search algorithm that is quadratically faster than its classical counterpart. More than a decade later, Harrow, Hassidim, and Lloyd proposed a quantum algorithm for solving systems of linear equations, now known as the HHL algorithm. With an emphasis on the circuit model, this work provides a detailed description of all these remarkable algorithms.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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