The field of quantum computing is developing at a rapid pace, and one can expect paradigm-shifting advances in coming years. The goal of this chapter is for the reader to understand fully the language and basic concepts of quantum information science needed to engage in research and development in this very exciting field in the future. We will apply the mathematical machinery we have acquired so far to develop the quantum counterparts to the classical notions of bits, logic gates, circuits, and algorithms. We will also review some of the promising examples of quantum hardware for physically realizing quantum information processing.
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