Now that we have the mathematical and physical preliminaries under our belt, we can move on to the nuts and bolts of quantum computing. At the heart of a computer is the notion of a bit. Quantum computers use a generalization of the concept of a bit called a qubit which shall be discussed in section 5.1. Bits are manipulated by classical (logical) gates. In section 5.2, classical gates are presented from a new and different perspective. From this angle, it is easy to formulate the notion of quantum gates which manipulate qubits. As mentioned in chapters 3 and 4, the evolution of a quantum system is reversible, i.e., manipulations that can be done must also be able to be undone. This “undoing” translates into reversible gates. In section 5.3, we deal with reversible gates and then move on to conclude with quantum gates in section 5.4. Reader’s Tip. Discussion of actual physical implementation of qubits an
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