1. Quantum Computation
권민호
Yonsei Univ.

2. “Hilbert Space is a big Place”
Digital Computer
N bits
N bits 1
Digital Computers in parallel
N bits m
N bits m 2
Quantum computer: Quantum parallelism N
N qubits
N qubits
“Hilbert Space is a big Place”
- Carlton Caves -

3. Classical Computing 5 4 3 2 1 3
Quantum Computing(Parallelism)
|1>
|2>
|3>
|3>
|4>
|5>

4. Quantum Algorithms
[Feynman] Simulation of Quantum Physical Systems with HUGE Hilbert space ( 2ⁿ-D )
e.g. Strongly Correlated Electron Systems
[Peter Shor] Factoring Integers, Period finding
tquantum ∝ N tclassical ∽ Exp[N ]
[Grover] Database Searching
tquantum ∝ √N <tclassical> ∽ N/2 3
1/3

5. Classical computing Quantum computing INPUT OUTPUT GATE OUTPUT U INPUT
U : Unitary Transform

6. Classical Computing
GATE
Ex) ADDER
INPUT
OUTPUT

7. Quantum Computing GATE Ex) U1 U2 time U1 U2 U3 INPUT OUTPUT |ψ₁>
|ψ₂>
U : Unitary transformation
Measurements

8. How it works? :Grover Algorithm
Initial state : Equal Superposition with n qubits
…………
N states ( or keys)

9. How it works? : Grover Algorithm(cont’d)
Oracle (Unitary Operator) : O
O : Oracle

10. How it works? : Grover Algorithm(cont’d)
Apply Grover operator G to
…………
…………

11. How it works? : Grover Algorithm(cont’d)
Apply Grover operator G to
…………
…………

12. How it works? : Grover Algorithm(cont’d)
Apply Grover operator G to for √N times,
Can you see THE OTHER KEYS?
…………
Finally, Measure the state!

13. # of required Qubits for Algorithm

16. References
Quantum Computation and Quantum Information – Nielsen & Chuang
양자컴퓨터Q- 조지 존슨
우주, 또 하나의 컴퓨터 – 톰 지그프리트
Decoding the universe - Charles Seife
Quantum Information and Computation(Caltech lecture) – John Preskill
Quantum Computing (UCB lecture) – Umesh Vazirani
PPT material –김재완 / 이순칠 KIAS Winter School on Quantum Information Science