The Phase of the “1” - Brain Theory from a Circuits and Systems Perspective - page 172

References

1. Burger JR (2011) Neural networks that emulate qubits. NeuroQuantology 9:910-916
2. Pittenger AO (1999) An introduction to quantum computing algorithms. Birkhauser, Boston,
MA
3. Burger JR (2011) Symmetric and anti-symmetric quantum functions. arXiv:cs/0304016, 13
June 2011
4. Nielson MA, Chuang IL (2000) Quantum computation and quantum information, Cambridge
series on information and the natural sciences. Cambridge University Press, Cambridge
[Paperback]

Self-Study Exercises

(If you desire to keep a record of your efforts, please show a couple of steps leading
to the answers.)

The Phase of the 1

1. What is observed after sampling?

[1 1] 0 (ANS. True with 50 % chance; false with 50 % chance)

(a) η

1] 0 (ANS. True with 50 % chance; false with 50 % chance)

(b) η [1

11] 0 using transforms as in the text to
determine its properties after a readout? (ANS. The transform gives [0

2. What is observed for the tagged list η [

1] 0 but
the negative sign is not seen. One reads out a true. So this is the result of a
nonconstant binary function, an inverter)

Symmetric and Antisymmetric Function Determination

3. List a truth table for the following:

(a) NOT function in shorthand form. (ANS. 1 0; means as the input counts in
binary up 0 1 the output follows as 1 0)
(b) All symmetric and antisymmetric functions for n

¼ 2, in shorthand form.

2 n or 8 functions and so there
are 8 truth tables: “0000, 0011, 0101, 0110, 1001, 1010, 1100, 1111”).
(c) Label the above functions to be symmetric or antisymmetric, and regular or
complementary (positive or negative). (ANS. s, a, a, s, s, a, a, s; +, +, +,+,

Place them in numerical order (there are 2

,

, , )