Successive action of gates

Two successive operations are two unitary gates, say A and B, acting one

after another. Algebraically, we represent the resultant by the action of the

usual matrix product of the two gates:

|ψi

A

−→ A|ψi

B

−→ BA|ψi. (7.13)

Note that the order of the gates is important. Operators do not in general

commute. The circuit representation of this process is like a time sequence,

and the order of gates is obvious