Basics on Quantum Computing

1. Quantum Computing
(picture coming soon)

2. We’ll hopefully cover:
Basic quantum theory of superposition
Basics of quantum computer
Applications
More specific operations on quantum
computer (√NOT), entangled NOT

3. Basic quantum mechanics
Superposition
● Electrons, along with all other fundamental particles,
have angular momentum
● The direction of their angular momentum is the direction
of their “spin”

4. ● The spin of an electron can be measured by shooting
them through an electric field (spin up means that it is
deflected one way, and spin down means that it is
deflected the other
● If we shot in a beam of electrons, we’d expect the spins
to be random
● Based on this, what might the final distribution of the
electrons look like?

5. Observed (!!!)
Expected

6. What does this mean???
● Btw, the electrons do not all have spins of
perfectly up and down - the results are the
same if we rotate the detector
● This means that, no matter what orientation
electrons are shot in, they’ll come out as up
or down when measured

7. So are the electrons that are in
between up or down?
● Neither! They’re in a superposition!
● In quantum notation, if 1 is up and 0 is down,
then the superposition is written a|0> + b|1>
● where “a” and “b” are the magnitudes, and
a^2 and b^2 are the respective probabilities
of the particle being 0 or 1 (this is kind of
weird, but it’ll be important later)

8. Quantum Computing!
● We can utilize the superposition property of
electrons
● Conventional computers work with
transistors - they are binary
10

9. Why are quantum computers better?
http://www.tubechop.com/watch/5143924
(I don’t like this video)

10. Applications
● Most popular method of cryptology - The factoring of
large numbers
● Factoring big numbers takes a loooooooooooooooong
time on a conventional computer
● However, Peter Shor came up with a method of
factoring that would take a reasonable amount of time
on a quantum computer (Shor’s algorithm)
● This means a lot of money is involved - motivation for
government and big corporations to develop quantum
computer before the bad guys do

11. Specific Operations - √NOT
● NOT operation flips the value of the bit (1 ->
0, and 0 -> 1)
● √NOT * √NOT = NOT
^nonsense?

12. What does √NOT mean
e-
1
e- e-
|0> + |1>
(superposition)
0
NOT
√NOT√NOT

13. Significance
● Allows us to put bits into superposition and
back
● When we read information, it has to be not a
superposition (otherwise it’s gibberish)

14. Entangled NOT
What happens if we put a superpositioned
particle into a NOT so that another bit takes on
the opposite value?
If the first particle is measured to be 1, the
other particle must be 1
If the first particle is measured to be 0, the
other particle must be 0

15. The particles are entangled - neither value is
known, but we do know that they are the same
value
Written as:
|01> + |10>
So it is a superposition between 0&1, and 1&0

16. END