Parameters Of Controlled-Not

When you press the OK button in this window, the computer checks that

the focus node has precisely two parents,
each parent has precisely 2 states, 0 and 1, in that order.

If these conditions are satisfied, the above window closes. Furthermore, the states and amplitudes stored in memory for the focus node are changed. If the conditions are not satisfied, the above window remains open, the states and amplitudes are not changed, and a warning message appears on the screen.

Consider, for example, what will happen if the above window is closed with the above settings:

Suppose M₁, M₂, N₁, N₂ are elements of {0,1}. The Parent Nodes table of the Node Prior-Info window will display the two parent nodes in a certain order. Say M₁ is the state of the first parent P₁, and M₂ is the state of the second parent P₂. Define (N₁, N₂) in terms of M₁ and M₂ as follows.

M₁ M₂ (N₁,N₂)

0 0 (0,0)

0 1 (0,1)

1 0 (1,1)

1 1 (1,0)

This table may be described by saying that

N₁ = M₁ and M₂ is transformed into N₂ ,
P₁ (the "control" bit) causes P₂ (the "target" bit) to flip (i.e., to change from 0 to 1 or vice versa) whenever M₁ is 1, and
P₁ has no effect on P₂ whenever M₁ is 0.

Quantum Fog gives names N₁N₂ (i.e., 00, 01, 10 and 11) to the states of the Controlled-Not. When the states M₁ and M₂ are given by a particular row of the above table, Quantum Fog assigns unit amplitude to the state N₁N₂ shown in that row, and it assigns zero amplitude to all the other states.

More information about Controlled-Nots can be found in the document entitled "Quantum Fog Library Of Essays" that accompanies this manual.

[Table Of Contents]