9.3 Building blocks and universality
In section 2.4or gate from nand gates. nand is universal in that we can create all the other classical logic gates from it. For example,
This means any software we build for classical computers could ultimately be constructed from millions of nand gates. That would be horribly inefficient. There are higher-level gates and circuits in modern processors that are tremendously faster.
The basic CNOT acts like a xor on the standard kets.
This maps the basis kets in this way:
. More than simply a logical operation, this implements addition mod 2. That is, this standard gate does a basic arithmetic operation ‘‘⊕’’. For example, |1⟩ ⊕ |1⟩ = |0⟩ and
(a |0⟩ + b |1⟩) ⊕ |1⟩ = a |0⟩ ⊕ |1⟩ + b |1⟩...
