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 PresentationTRANSCRIPT
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Quantum ComputerQuantum Computer Quantum ComputerQuantum Computer
電機四 鄭仲鈞電機四 鄭仲鈞
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Outline• Quantum Computer• Quantum Computing• Implement of Quantum Computer• Nowadays research of Quantum com
puter
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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:
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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.
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Outline• Quantum Computer• Quantum Computing• Implement of Quantum Computer• Nowadays research of Quantum
computer
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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…
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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
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Thank you!!