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：量子计算正在飞速发展，迫使我们重新审视、重写和更新这一领域的理论基础。《基础量子算法》重新审视了最早的量子算法。旅程始于1985年，Deutsch试图同时评估两个定义域点上的函数。然后，在1992年，Deutsch和Jozsa创造了一种量子算法，用于确定一个布尔函数是常数还是平衡的。接下来的一年，Bernstein和Vazirani发现，相同算法可以用于在线性布尔函数集合中识别特定的布尔函数。1994年，Simon提出一种新颖的量子算法，以指数方式比同一问题的任何经典算法更快地确定函数是一对一还是一对二。同年，Shor开发了两个划时代的量子算法，用于整数因子分解和计算离散对数，对广泛使用的密码方法构成威胁。1995年，Kitaev提出了另一种Shor算法的替代版本，在众多其他应用中得到了证明。随后的一年，Grover设计了一种量子搜索算法，其速度相当于其经典等效物的平方倍。本文着重介绍电路模型，详细描述了所有这些显著的算法。