Quick Reference

Cheatsheet

Core Concepts

Qubit

Quantum bit. Can be |0⟩, |1⟩, or superposition of both.

Superposition

Qubit in multiple states simultaneously: α|0⟩ + β|1⟩

Entanglement

Qubits correlated so measuring one affects the other instantly.

Measurement

Collapses superposition to |0⟩ or |1⟩. Probabilistic outcome.

Common Gates

Gate

Qiskit

Action

X (NOT)

qc.x(0)

Flip |0⟩ ↔ |1⟩

H (Hadamard)

qc.h(0)

Create superposition

CNOT

qc.cx(0, 1)

Flip target if control = |1⟩

qc.z(0)

Phase flip (|1⟩ → -|1⟩)

RY(θ)

qc.ry(θ, 0)

Rotate around Y-axis

Measure

qc.measure(0, 0)

Collapse and read qubit

Qiskit at a Glance

# Setup
from qiskit import QuantumCircuit
from qiskit_aer import AerSimulator
from qiskit.visualization import plot_histogram

# Create circuit with 2 qubits, 2 classical bits
qc = QuantumCircuit(2, 2)

# Add gates
qc.h(0)           # Hadamard on qubit 0
qc.cx(0, 1)       # CNOT: control=0, target=1
qc.measure([0,1], [0,1])

# Draw the circuit
qc.draw('mpl')

# Run simulation
simulator = AerSimulator()
job = simulator.run(qc, shots=1000)
result = job.result()
counts = result.get_counts()

# Plot results
plot_histogram(counts)

Key Formulas

Qubit State

|ψ⟩ = α|0⟩ + β|1⟩ where |α|² + |β|² = 1

Measurement Probability

P(0) = |α|², P(1) = |β|²

Bell State

|Φ+⟩ = (|00⟩ + |11⟩) / √2

Grover Iterations

Optimal iterations ≈ (π/4)√N

Common Patterns

Create Superposition

qc.h(0)

Create Bell State

qc.h(0); qc.cx(0,1)

Flip a Qubit

qc.x(0)

Measure All

qc.measure_all()

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