This textbook presents the elementary aspects of quantum computing in a mathematical form. It is intended as core or supplementary reading for physicists, mathematicians, and computer scientists taking a first course on quantum computing. It starts by introducing the basic mathematics required for quantum mechanics, and then goes on to present, in detail, the notions of quantum mechanics, entanglement, quantum gates, and quantum algorithms, of which Shor's factorisation and Grover's search algorithm are discussed extensively. In addition, the algorithms for the Abelian Hidden Subgroup and Discrete Logarithm problems are presented and the latter is used to show how the Bitcoin digital signature may be compromised.

这本教科书以数学形式介绍量子计算的基本方面。本书旨在作为物理学家、数学家和计算机科学家学习量子计算第一门课程的核心或补充读物。首先介绍量子力学所需的基本数学，然后详细介绍量子力学、纠缠、量子门和量子算法的概念，其中广泛讨论了Shor的因式分解和Grover的搜索算法。此外，还介绍了阿贝尔隐子群和离散对数问题的算法，后者用于说明比特币数字签名可能受到的危害。