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.

翻译：量子计算正以惊人的速度发展，迫使我们不断重访、重写并更新其理论基础。本文《基本量子算法》回顾了最早的量子算法。1985年，Deutsch首次尝试同时评估函数在两个定义域点的取值；1992年，Deutsch与Jozsa提出一种能判定布尔函数是常数函数还是平衡函数的量子算法；次年，Bernstein与Vazirani发现本质上相同的算法可用于从线性布尔函数集合中识别特定布尔函数。1994年，Simon提出一种创新量子算法，能以指数级速度超越任何经典算法，判断函数是单射还是二对一映射；同年，Shor开发出两项突破性量子算法——整数分解与离散对数求解，对主流密码学方法构成威胁。1995年，Kitaev提出基于相位估计的替代方案，该方案在众多应用中展现出重要价值；次年，Grover设计出量子搜索算法，其速度较经典算法实现二次加速。十余年后，Harrow、Hassidim与Lloyd提出求解线性方程组的量子算法，即现今广为人知的HHL算法。本文以电路模型为重点，对所有上述卓越算法进行了详细阐述。