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title

Quantum Computing

매 한 줄

"매 superposition + entanglement = exponential parallelism.". 1981년 Feynman이 양자 시뮬레이션 limitation 제기. 2019 Google Sycamore quantum supremacy → 2024 IBM Heron 156-qubit, 2026 fault-tolerant prototype 등장. NISQ era에서 early fault-tolerant 로 전환 중.

매 핵심

매 Qubit Model

Classical bit: {0, 1}. Qubit: α|0⟩ + β|1⟩, |α|² + |β|² = 1.
N qubits → 2^N complex amplitudes (exponential state space).
Measurement: collapse to basis state probabilistically.

매 Three Quantum Resources

Superposition: Hadamard gate H|0⟩ = (|0⟩+|1⟩)/√2.
Entanglement: Bell state (|00⟩+|11⟩)/√2 — non-local correlation.
Interference: amplitudes add/cancel to amplify correct answer.

매 응용

Shor's algorithm — RSA factoring in polynomial time.
Grover's search — O(√N) database search.
VQE/QAOA — chemistry simulation, combinatorial optimization.
Quantum machine learning (kernel methods).

💻 패턴

Bell State (Qiskit)

from qiskit import QuantumCircuit, transpile
from qiskit_aer import AerSimulator

qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])

sim = AerSimulator()
result = sim.run(transpile(qc, sim), shots=1024).result()
print(result.get_counts())  # ~50% '00', ~50% '11'

Grover's Algorithm (2-qubit)

from qiskit import QuantumCircuit
import numpy as np

def grover_2q(marked_state):
    qc = QuantumCircuit(2)
    qc.h([0, 1])
    # Oracle: phase flip on marked
    if marked_state == '11':
        qc.cz(0, 1)
    # Diffuser
    qc.h([0, 1]); qc.x([0, 1])
    qc.cz(0, 1)
    qc.x([0, 1]); qc.h([0, 1])
    return qc

VQE for H2 ground state

from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_algorithms import VQE
from qiskit_algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.circuit.library import UCCSD, HartreeFock

driver = PySCFDriver(atom='H 0 0 0; H 0 0 0.735')
problem = driver.run()
ansatz = UCCSD(problem.num_spatial_orbitals, problem.num_particles, ...)
vqe = VQE(Estimator(), ansatz, SLSQP())
result = vqe.compute_minimum_eigenvalue(problem.hamiltonian.second_q_op())

QAOA for Max-Cut

from qiskit_optimization.applications import Maxcut
from qiskit_algorithms import QAOA

graph = nx.gnp_random_graph(5, 0.5)
problem = Maxcut(graph).to_quadratic_program()
qaoa = QAOA(sampler=Sampler(), optimizer=COBYLA(), reps=3)
result = qaoa.compute_minimum_eigenvalue(problem.to_ising()[0])

Quantum Phase Estimation skeleton

def qpe(unitary, n_counting, eigenstate):
    qc = QuantumCircuit(n_counting + eigenstate.num_qubits)
    qc.h(range(n_counting))
    qc.append(eigenstate, range(n_counting, qc.num_qubits))
    for q in range(n_counting):
        qc.append(unitary.power(2**q).control(),
                  [q] + list(range(n_counting, qc.num_qubits)))
    qc.append(QFT(n_counting, inverse=True), range(n_counting))
    return qc

Error mitigation (Zero Noise Extrapolation)

from mitiq import zne
def executor(circuit): return run_on_hw(circuit)
mitigated = zne.execute_with_zne(circuit, executor,
                                  scale_factors=[1, 3, 5])

매 결정 기준

상황	Approach
Cryptanalysis (factoring)	Shor (need fault-tolerant, 2030+)
Combinatorial optim, NISQ	QAOA + warm-start
Chemistry / materials	VQE with UCCSD ansatz
Search w/ structure	Quantum walks, Grover variants
ML kernels	Quantum feature maps (caveat: limited speedup proof)

기본값: 2026 production은 매 hybrid quantum-classical (VQE/QAOA) on real hardware via IBM Quantum / IonQ / Quantinuum.

🔗 Graph

부모: Theoretical-Computer-Science · Linear-Algebra-Foundations
변형: Quantum-Computing
응용: Practical-Cryptography · Combinatorial-Optimization

🤖 LLM 활용

언제: hardware-aware compilation 설명, ansatz 설계 brainstorm, error mitigation strategy 추천. 언제 X: 매 large-scale circuit simulation 직접 실행 (use Qiskit/Cirq locally), 매 hardware-specific calibration data.

❌ 안티패턴

Quantum hype: 매 "quantum solves NP" — 매 BQP ⊄ NP-complete (likely).
Decoherence ignore: shallow circuits 만 NISQ 에서 의미. Deep circuits → noise dominate.
Classical baseline 무시: 매 tensor network / Monte Carlo 가 매 quantum 보다 fast 한 경우 多.
Measurement overhead: 매 expectation value estimation 위해 1000s shots 필요.

🧪 검증 / 중복

Verified (Nielsen & Chuang Quantum Computation and Quantum Information; IBM Qiskit textbook 2025).
신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — qubit model, Bell/Grover/VQE/QAOA/QPE 패턴, NISQ→FT 전환 정리

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