Chapter 5: Architecture - Computer and Information Science - CUNY

14 CHAPTER 5. ARCHITECTURE
Combination of sequential and parallel operations gates/matrices will be
circuits. We will, of course, construct some really complicated matrices, but
they will all be decomposable into the sequential and parallel composition of
simple gates.
Exercise 5.2.5 In Exercise CITE EXERCISE, we proved that for matrices of
the appropriate sizes A, A ′ , B and B ′ we have the following equation
(B ⊗ B ′ ) ⋆ (A ⊗ A ′ ) = (B ⋆ A) ⊗ (B ′ ⋆ A ′ ). (5.44)
What does this correspond to in terms of performing different operations to
different (qu)bits? Hint: Consider the following figure
A
B
(5.45)
A ′ B ′
Example 5.2.1 Let A be an operation that takes n inputs and gives m outputs.
Let B take p < m of these outputs and leave the other m − p outputs alone. B
outputs q bits
/ n A
/ p B / q
/ m−p (5.46)