1. Quantum Computing and Quantum Programming Language
Choon Oh Lee
ISILab, KAIST

2. Motivation Moore’s Law
Number of transistors per square inch doubles every two years.
Expected be broken down in 2020
Atomic scales are reached
Incoherent by any particle
Solutions
Fatalists: Noise-based Computing
Optimists: Quantum Computing

3. various candidates (Ion trap, NMR, etc.)
Bit vs Qubit
Value
Realization
Computation
Universal component or
NAND and NOR gate 1
various candidates (Ion trap, NMR, etc.)
Controlled Not gate
5 V
0 V 1 1 S
Q. Circuit
ADDER S
Measuring 1 1

4. How’s qubit possible? The legendary experiment
By David Wineland and Christopher Monroe
Steps
Pin Barium ion in vacuum room
Optical freezing on ion to deactivate it
Expose ion on laser pulse for certain time
Barium ion had superposition
Slightly push ion using laser beam
One ion existed on two different spots
Remarks
Superposition is collapsed in 25~50 microsecond
NIST scientists succeed to make first controlled not gate based on this experiment

5. Conceptual Models Quantum Circuit Matrix Mechanics Computational Model
Algorithmic Model
Quantum Circuit
Matrix Mechanics A B D M C M
4 by 4
2 by 2
2 by 2
2 by 2
2 by 2
2 by 1
2 by 1

6. Quantum Gates
Pauli Gates
Identity (I)
Not Gate (X)
Y Gate
Z Gate

7. Quantum Gates
Hadamard Gate (H)
Make a qubit superpositioned.

8. Quantum Gates Controlled Not Gate (cNot)
Apply NOT gate on second bit when first bit is 1.

9. Quantum Gates Measurement (M) Technically, it’s not a gate
It measures a qubit to determine its value
Output of measurement would be 0 or 1
Probability to be 0:
Probability to be 1:
After it measures qubit, qubit becomes just bit

10. Algorithms Quantum Teleportation Qubits cannot be copied or moved
How to teleport a qubit
Prepare two entangled qubits,
Alice and Bob take each qubit initially
Alice wants to send an another qubit to Bob

11. Algorithms Quantum Teleportation H M M Z Originalqubit Alice’s qubit
Bob’s qubit Z
Same qubit

12. Algorithms Quantum Teleportation Initial state H M M Z Originalqubit
Alice’s qubit M
Bob’s qubit Z
Same qubit

13. Algorithms Quantum Teleportation Previous state Current state H M M Z
Originalqubit H M
Alice’s qubit M
Bob’s qubit Z
Same qubit

14. Algorithms Quantum Teleportation Previous state Current state H M M Z
Originalqubit H M
Alice’s qubit M
Bob’s qubit Z
Same qubit

15. Algorithms Quantum Teleportation Rearrange current state H M M Z
Originalqubit H M
Alice’s qubit M
Bob’s qubit Z
Same qubit

16. Algorithms Quantum Teleportation Measure first two qubits H M M Z
Originalqubit H M
Alice’s qubit M
Bob’s qubit Z
Same qubit

17. Algorithms Grover’s Search Algorithm
Searching desired items from database
Instead of checking every items in database, algorithm increases probabilities that desired items can be found decreasing others’
Idea is simple, but point is quantum parallelism!

18. Algorithms Grover’s Search Algorithm 1 2 3 4 5 6 7 Probability1 2 3 4 5 6 7
Probability
(amplitude)2
1. Apply Hadamard gates to make superposition 1 2 3 4 5 6 7
Probability
(amplitude)2

19. Algorithms Grover’s Search Algorithm 1 2 3 4 5 6 7 Probability1 2 3 4 5 6 7
Probability
(amplitude)2
2. Apply function f 1 2 3 4 5 6 7
Probability
(amplitude)2

20. Algorithms Grover’s Search Algorithm 1 2 3 4 5 6 7 Probability1 2 3 4 5 6 7
Probability
(amplitude)2
Average line
3. Flip probability based on average point 1 2 3 4 5 6 7
Probability
(amplitude)2
Average line

21. Algorithms Shor’s Factoring Algorithm
Great algorithm that attracted the world’s attention to quantum computing
Proposed shortcut to break RSA system
The source of RSA’s power is hardness of factorization of a big number which is product of two prime numbers
Best known way to factor a number, N
Find a and b where N divides (a2 – b2)
If N doesn’t divide (a + b) and (a – b),
Then, gcd(N, (a + b)) is one of factors of N
Another factor is then N / gcd(N, (a + b))

22. Algorithms Shor’s Factoring Algorithm Algorithm
input: an odd integer n
Choose g in [2…n-1] randomly
Calculate d = gcd(g, n)
If d ≠ 1, return d
Calculate r where gr = 1 (mod n)
If r is even, and n doesn’t divide gr/2+1 or gr/2-1, then return gcd(n, gr/2+1)
Re-find r or g
Shor used superpositioned qubits to represent g and QFT to calculate r