The Phase of the “1” - Brain Theory from a Circuits and Systems Perspective - page 173

4. Apply the procedure given in the text to identify the following function: “1001”
when assumed applied to a multivibrator. (ANS. a 1 ¼ 1; a 2 ¼ 1; b 1 ¼ 1,

b 2 ¼ 1 which would be observed as 11 )

5. Can you discover another way to express the last transformation that identifies a
symmetric and antisymmetric function? (HINT: Multiply the tagged list [

111

1] 0 by H n with n

¼ 2.)

6. What is the potential savings in effort for symmetric-antisymmetric function
identification when comparing simulated qubit versus classical function identi-
fication assuming n

¼ 10? (Roughly 1 evaluation of the function versus up to

2 10

1,024 evaluations)
(a) Why might classical identification be less than 2 n ? (ANS. Symmetry might
be used to advantage)

¼

Satisfiability

7. Assume a truth table as follows: “0001.” Trace through the listing method given
in the text to find what satisfies this function. (ANS. a 1 ¼ 1, a 2 ¼ 1, b 1 ¼ 1,

b 2 ¼ 1 or what is read is ab ¼ 11 )

Data Packing

8. Use combinations of [1 0] 0 ,[01] 0 , and η ¼ η [1 1] 0 assuming three simulated

qubits:

... η ,

η , η ) (a) Count with these codes (ANS. 0, 0, 0; 1, 1, 1;

...

(b) How many codes are there? (ANS. 2 n + n{2 n1 +2 n2 , ,2 1 }+1 ¼ 29)

[1 1] 0 . (HINT: Several qubit readouts are necessary.) 9. Devise a way to detect η