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: … 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:  Amplitude (possibility)  Orthogonal Basis (Specific State) Ex: Sup State: Possible States:

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.

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 13/16

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.

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 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 time qubits

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)

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 computer (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

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

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

What is quantum dot? A small dot structure including 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 MHz trap 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!!