Quantum Basics Recap

Concept	Description	Formula / Note
Qubit	Quantum bit — superposition of	0⟩ and
Superposition	Qubit in multiple states simultaneously	α, β are complex amplitudes
Measurement	Collapses state to classical bit	Prob(0) = |α|²
Entanglement	Correlation between qubits	Used in Bell states
Gate	Unitary operation on qubits	e.g. H, X, Z, CNOT

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Quantum AI Core Concepts

Concept	Description
VQC (Variational Quantum Circuit)	Hybrid model where parameters are optimized by a classical optimizer.
Quantum Feature Encoding	Maps classical data to quantum states (Amplitude, Angle, Basis Encoding).
Hybrid Model	Combines classical NN + quantum circuit (e.g., classifier or encoder).
Quantum Kernel Method	Computes quantum-based similarities in feature space.
Quantum GANs	Generator and discriminator partly implemented as quantum circuits.

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PennyLane Quick Commands

Task	Code Snippet
Import & Device	import pennylane as qmldev = qml.device("default.qubit", wires=2)
Create a circuit	@qml.qnode(dev)def circuit(params): qml.RY(params[0], wires=0)
Measure expectation	return qml.expval(qml.PauliZ(0))
Optimize	opt = qml.GradientDescentOptimizer(stepsize=0.1)params = opt.step(cost, params)
Draw circuit	qml.draw(circuit)(params)

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Qiskit Essentials

Task	Code
Setup	from qiskit import QuantumCircuit, Aer, transpile, assemble, execute
Basic circuit	qc = QuantumCircuit(2); qc.h(0); qc.cx(0,1); qc.measure_all()
Run simulator	sim = Aer.get_backend('aer_simulator'); result = sim.run(qc).result()
View results	result.get_counts()
Visualize	qc.draw('mpl')

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Hybrid Model Example (Quantum + Classical)

import pennylane as qml
from sklearn.datasets import make_classification
from sklearn.linear_model import LogisticRegression

# Quantum feature map
dev = qml.device("default.qubit", wires=2)
@qml.qnode(dev)
def quantum_features(x1, x2):
    qml.AngleEmbedding([x1, x2], wires=[0,1])
    qml.CNOT(wires=[0,1])
    return [qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1))]

# Classical data
X, y = make_classification(n_samples=50, n_features=2)
X_q = [quantum_features(a,b) for a,b in X]
model = LogisticRegression().fit(X_q, y)

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Quantum AI Platforms

Platform	Tools / SDKs	Highlights
IBM Quantum	Qiskit	Free cloud access, real hardware
AWS Braket	Braket SDK	Supports multiple hardware providers
Google Quantum AI	Cirq	Research-grade circuits
PennyLane Cloud	PennyLane	Hybrid integration with TensorFlow & PyTorch

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Quick Reference Formulas

Task	Formula / Concept
Quantum State Norm	|α|² + |β|² = 1
Measurement Probability	P(0) = |α|², P(1) = |β|²
Rotation Gate	RY(θ) = exp(-iθY/2)
Expectation Value	⟨ψ|Z|ψ⟩
Variational Loss	L(θ) = ⟨ψ(θ)|H|ψ(θ)⟩

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Ethical & Responsible Quantum AI

• Always disclose limitations of hybrid models.
• Validate outputs with classical baselines.
• Avoid bias amplification from training data.
• Ensure transparency in explainability.

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Bonus Tip

“Quantum AI is not about replacing classical AI — it’s about augmenting it to solve problems classical systems can’t scale to.”

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Quantum_AI_Cheatsheet.pdf