A gate for a Quantum Computer Let CNOT=(1000010000010010)\text{CNOT} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix}CNOT=1000010000010010 Example CNOT∣a,b⟩=∣a, b⊕a⟩\text{CNOT}\ket{a,b} = \ket{a,\, b \oplus a}CNOT∣a,b⟩=∣a,b⊕a⟩ where ⊕\oplus⊕ is addition mod 2Quantum Gate Controlled u