NOT (X) Gate
Formally, the NOT gate belongs to the Pauli family of quantum gates and is also called the Pauli-X gate. Hence, the gate is often labeled with an X. (In Universal Quantum Gates, we’ll see why the Pauli-X or X gate is fittingly called the NOT gate.) The other gates in this family are the Pauli-Y and the Pauli-Z gates, which we’ll discuss in Chapter 7, Small Step for Man—Single Qubit Programs. For more information, see Section 2.4.1.1 in Explorations in Quantum Computing [Wil11].
Think of the NOT gate as a switcher—its sole purpose is to replace the state on the qubit from one to the other. Although this seems simple, this gate plays a large role in quantum programs.
In a binary system, if, for instance, a bit is “NOT 1,” ...
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