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Quantum Computer

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

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Quantum Computer

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  1. Quantum Computer 電機四 鄭仲鈞

  2. Outline • Quantum Computer • Quantum Computing • Implement of Quantum Computer • Nowadays research of Quantum computer

  3. 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…

  4. Quantum Computer • Qubit( Quantum bit ): 0 and 1 bit bit qubit and = ? 0 1 • I’m 0 and 1 4qubits:  ????(weird thing) In fact, it can represent 0~15 simultaneously

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

  6. Uncertainty of State • Electrons 2 Bits 2 Qubits 1 00/1 0/1 Material wave State superposition

  7. Superposition • Superposition state: Amplitude (possibility) • OrthogonalBasis (Specific State) • Ex: Sup State: Possible States:

  8. A property of qubit Any 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.

  9. Outline • Quantum Computer • Quantum Computing • Implement of Quantum Computer • Nowadays research of Quantum computer

  10. Now thatwe have qubit… • A random number generator?? Must have a method to get the answer we want. 1/16 1/16 1/16 13/16

  11. Interference as calculation • Wave property: Two Qubit(electron) can interfere each other. Constructive: % up Destructive : % down We can use wave interference as a calculation method.

  12. 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?

  13. 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 time qubits

  14. 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

  15. Shor's algorithm(con’t) • An example:

  16. 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 computer (qubit) is really hard…

  17. Outline • Quantum Computer • Quantum Computing • Implement of Quantum Computer • Nowadays research of Quantum computer

  18. Implement of qubits • 1. Nuclear magnetic resonance (NMR) • 2. Quantum dot • 3. Ion trap A Bloch sphere as a schema of a qubit

  19. NMR Nucleus’ magnetic moment as qubit Controlled by EM wave Measured by Nuclear magnetic resonance 2C +5F = 7 qubits Not enough qubits

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

  21. 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

  22. 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.

  23. Ion trap 4 rod electrodes AC 1kv MHz trap the ions Ions (cold trapped) End-rings Charged to prevent escaping No AC electric field, spin direction as qubit

  24. The problem is… • Environment influences the states of qubits. • It will make the result incorrect. By experiments, Ion trap is the most potential one.

  25. Outline • Quantum Computer • Quantum Computing • Implement of Quantum Computer • Nowadays research of Quantum computer

  26. 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)

  27. 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

  28. 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

  29. Thank you!!

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