Quantum computing is evolving so rapidly that it forces us to revisit, rewrite, and update the foundations of the theory. 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 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 determined whether a function was 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 the widely used cryptography methods. In 1995, Kitaev proposed an alternative version of Shor's algorithms that proved valuable in numerous other applications. The following year, Grover devised a quantum search algorithm that was quadratically faster than its classical equivalent. With an emphasis on the circuit model, this work provides a detailed description of all these remarkable algorithms.

翻译：量子计算发展如此迅速，迫使我们重新审视、修订并更新该理论的基础。基础量子算法回顾了最早的量子算法。这段历程始于1985年，Deutsch尝试同时在两个定义域点评估一个函数。随后在1992年，Deutsch和Jozsa提出了一种量子算法，用于判断布尔函数是常数函数还是平衡函数。次年，Bernstein和Vazirani意识到同一算法可用于在线性布尔函数集合中识别特定布尔函数。1994年，Simon引入了一种新型量子算法，其判断函数是一对一函数还是二对一函数的速度比任何经典算法都呈指数级提升。同年，Shor开发了两种开创性量子算法，分别用于整数分解和计算离散对数，对当时广泛使用的密码学方法构成威胁。1995年，Kitaev提出Shor算法的替代版本，该版本在其他众多应用中证明极具价值。次年，Grover设计了一种量子搜索算法，其速度相较经典算法呈二次方提升。本文以电路模型为重点，详细描述了所有这些杰出算法。