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Quantum Computer Quantum Computer 電電電 電電電 電電電 電電電

Quantum Computer

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Quantum Computer. 電機四 鄭仲鈞. Outline. Quantum Computer Quantum Computing Implement of Quantum Computer Nowadays research of Quantum computer. Traditional Computer. bit: 0 or 1 4 bits data: 0000 0001 0010 0011 … represent 0~15 by the combination of 0 and 1 - PowerPoint PPT Presentation

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Page 1: Quantum Computer

Quantum ComputerQuantum Computer Quantum ComputerQuantum Computer

電機四 鄭仲鈞電機四 鄭仲鈞

Page 2: Quantum Computer

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

puter

Page 3: Quantum Computer

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…

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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

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

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Uncertainty of State• Electrons 2 Bits 2 Qubits

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

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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:

Page 8: Quantum Computer

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.

Page 9: Quantum Computer

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

computer

Page 10: 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

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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.

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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?

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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

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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

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Shor's algorithm(con’t)• An example:

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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…

Page 17: Quantum Computer

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

computer

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Implement of qubits• 1. Nuclear magnetic resonance

(NMR) • 2. Quantum dot• 3. Ion trap

A Bloch sphere as a schema of a qubit

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

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

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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

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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.

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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

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The problem is…• Environment influences the states of

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

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

computer

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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)

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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

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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

Page 29: Quantum Computer

Thank you!!