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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. It also treats the problem of error correction as well as giving a detailed exposition of adiabatic quantum computing. The book contains around140 exercises for the student, covering all of the topics treated, together with an appendix of solutions.
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