Chapter 5: Architecture - Computer and Information Science - CUNY

22 CHAPTER 5. ARCHITECTURE
|x〉
|x〉
• •
(5.61)
|y〉
• •
|y〉
|0〉
•
|0〉
|z〉
•
|z〉
|w〉
|w ⊕ (x ∧ y ∧ z)〉
One reason why the Toffoli gate is interesting is that it is universal. In
other words, with copies of the Toffoli gate, you can make any logical gate. In
particular, you can make a reversible computer using only Toffoli gates. Such a
computer would, in theory, neither use any energy nor give off any heat.
In order to see that the Toffoli gate is universal, we shall show that you can
make the AND and the NOT gate with it. The AND gate is obtained by setting
the bottom z input to |0〉. The bottom output will then be |x ∧ y〉.
|x〉
•
|x〉
(5.62)
|y〉
•
|y〉
|0〉
|x ∧ y〉
The NOT gate is obtained by setting the top two inputs to |1〉. The bottom