Quantum Computation 0541111 권민호 Yonsei Univ.

“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 -

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

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

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

Classical Computing GATE Ex) ADDER INPUT OUTPUT

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

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

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

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

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

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!

# of required Qubits for Algorithm

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