Preliminaries
Abstract
This chapter reviews the basic concepts from quantum mechanics and quantum computation required for reading the subsequent chapters. It first introduces the Hilbert space formalism of quantum mechanics and related mathematical tools. In particular, the basic postulates for description of the state space and dynamics of a quantum system, quantum measurements, and composite quantum systems are presented. Then formal definitions of quantum logic gates and circuits are given and several basic quantum gates are presented, including single quantum-bit gates, controlled gates and quantum multiplexors. Finally, two basic techniques for designing quantum algorithms, namely quantum parallelism and interference, are introduced. ...
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