Quantum Gate Introduction: NOT and CNOT Gates

We will introduce the first two quantum gates in this chapter. One is a one-qubit NOT gate and the other is a two-qubit CNOT gate. We will learn how to define a quantum gate. We will learn how they operate on an arbitrary quantum state through matrix multiplication and Dirac bra–ket notation operations. Matrix multiplication is important for implementing quantum computing simulators. Dirac bra–ket notation is important in gaining an intuitive understanding of the gates and designing new algorithms. We will also see the importance of determining the location of the most and least significant qubits in a multiple-qubit gate circuit.