Quantum ComputerQuantum Computer Quantum ComputerQuantum Computer

電機四 鄭仲鈞電機四 鄭仲鈞

Outline• Quantum Computer• Quantum Computing• Implement of Quantum Computer• Nowadays research of Quantum com

puter

Traditional Computer• bit: 0 or 1• 4 bits data: 0000 0001 0010 0011… represent 0~15 by the combination of 0 and 1 one combination one value 0000 0, 0001 1, 0010 2…

Quantum Computer• Qubit( Quantum bit ): 0 and 1 bit bit qubit

and = ?

0 1

4qubits:

????(weird thing)

I’m 0 and 1

In fact, it can represent 0~15 simultaneously

Qubit( Quantum bit)• Any thing that has quantum property can be a qubit. What quantum property? Uncertainty of States

Uncertainty of State• Electrons 2 Bits 2 Qubits

1 0 0/1 0/1 Material wave State superposition

Superposition• Superposition state:

in ,1....22

2

2

1

nn xxx ....2211

},....,,{ 21 nxxx

}1,0{

12

10

2

1

Amplitude (possibility)

Orthogonal Basis (Specific State)

• Ex: Sup State:

Possible States:

A property of qubitAny observation will force qubit into a certain state. Before observation: superposition of 0 and 1, but not pure 0 or 1 After observation: must be 0 or 1.

Outline• Quantum Computer• Quantum Computing• Implement of Quantum Computer• Nowadays research of Quantum

computer

Now that we have qubit…• A random number generator??

Must have a method to get the answer we want.

1/16

1/16

1/16

13/16

Interference as calculation

• Wave property:Two Qubit(electron) can interfere each other.Constructive: % up Destructive : % down We can use wave int

erference as a calculation method.

Factoring a big number • RSA, public-key cryptography method Public key N which is the product of two large prime numbers. One way to crack RSA encryption is by factoring N

Factor a number in 400 bits– Super computer take 1000000000 years– Quantum computer(1000qubits) only take few hours But how can it do that?

Quantum Parallelism• Traditional: N Choices. We have to calculate: 0, 1, 2, …N time to get correct answer. Quantum computer: N Choices into 1 value. N calculation completed at one time

T: 63÷1, 63÷2… 63÷8 ,calculate 8times

Q: 63÷ , parallel 8 values

calculate only 1 timequbits

Shor's algorithm• use conventional algorithm

factor a number N in O ( )• use Quantum Parallelism factor a number N in O ( )Note that < N (efficient!!)Constructive Interference: Find peak value (perhaps the solution) http://en.wikipedia.org/wiki/Shor's_algorithm

3

1

Ne

3)(logN3)(logN

Shor's algorithm(con’t)• An example:

We already have a method to break RSA…• Why do we still use RSA as a popular

public-key cryptography method? Because the implement of quantum c

omputer (qubit) is really hard…

Outline• Quantum Computer• Quantum Computing• Implement of Quantum Computer• Nowadays research of Quantum

computer

Implement of qubits• 1. Nuclear magnetic resonance

(NMR) • 2. Quantum dot• 3. Ion trap

A Bloch sphere as a schema of a qubit

NMRNucleus’ magnetic moment as qubitControlled by EM waveMeasured by Nuclear magnetic resonance 2C +5F = 7 qubits Not enough qubits

Quantum dotLithography and etching: Build 2D InGaAs surface. And then Etching the edge out.

What is quantum dot?A small dot structure including 1-100 electrons in it. The quantum dot’s scale must small than Fermi wavelength.Fermi wavelength In GaAs (Semiconductor)λf = 40nm In Al (metal)λf = 0.36nm

Where is the qubit?• (a). Add an extract electron as • (b). Electron spin up as spin down as

Recently find a new way: excited electron as

Electron density of a parabolic quantum dot with 6 electrons in a magnetic field.

Ion trap

4 rod electrodes AC 1kv MHztrap the ions

Ions (cold trapped)

End-rings Charged to prevent escaping

No AC electric field, spin direction as qubit

The problem is…• Environment influences the states of

qubits. • It will make the result incorrect. By experiments, Ion trap is the most potential one.

Outline• Quantum Computer• Quantum Computing• Implement of Quantum Computer• Nowadays research of Quantum

computer

Nowadays research• European :

– Information Society Technologies• United Kingdom:

– CQC( Centre for Quantum Computation)– Oxford, Cambridge

• Australian:Centre for Quantum Computer Technology

• Japan:ERATO (Exploratory Research for Advanced

Technology)

Stanford and IBM• First demonstration (in 2001) Shor's factoring algorithm • 7 qubits system to find the factor of 15• System tube including molecule that has 7 nuclear spins

Conclusion• Quantum computer is really powerful.• Although Quantum computer is hard

to implement, it is still realizable. • Quantum computer will be an

important research issue in the future.• It is fun to know more about such an interesting knowledge. A good experience

Thank you!!