Quantum Machine Learning — Deep Dive¶

Tested with: Quanta SDK v0.8.1

What You'll Learn¶

Build quantum classifiers, use quantum kernels, and understand feature maps.

Prerequisites¶

04 — Algorithms

QuantumClassifier — Variational Quantum Circuit¶

The QuantumClassifier uses a parameterized quantum circuit (PQC) trained with parameter-shift gradients:

from quanta.layer3.qml import QuantumClassifier
import numpy as np

# Simple binary classification
X = np.array([[0.1, 0.2], [0.8, 0.9], [0.2, 0.1], [0.9, 0.8]])
y = np.array([0, 1, 0, 1])

clf = QuantumClassifier(n_qubits=2, n_layers=2, seed=42)
result = clf.fit(X, y, epochs=20)
print(f"Accuracy: {result.accuracy:.0%}")
print(f"Parameters: {result.n_params}")

Feature Maps¶

Feature maps encode classical data into quantum states:

from quanta.layer3.qml import angle_encoding, zz_feature_map
from quanta.simulator.statevector import StateVectorSimulator
import numpy as np

x = np.array([0.5, 0.3])

# Angle encoding: x_i → RY(x_i)
sim_angle = StateVectorSimulator(2)
angle_encoding(sim_angle, x)
print(f"Angle encoding dim: {len(sim_angle.state)}")

# ZZ encoding: entangling feature map
sim_zz = StateVectorSimulator(2)
zz_feature_map(sim_zz, x)
print(f"ZZ encoding dim: {len(sim_zz.state)}")

Quantum Kernel¶

Compute quantum kernel matrices for kernel-based ML:

from quanta.layer3.qml import QuantumKernel
import numpy as np

X = np.array([[0.1, 0.2], [0.8, 0.9], [0.5, 0.5]])

kernel = QuantumKernel(n_qubits=2)
K = kernel.matrix(X)

print(f"Kernel matrix shape: {K.shape}")  # (3, 3)
print(f"K[0,0] (self-similarity): {K[0,0]:.4f}")  # ~1.0
print(f"K[0,1] (different points): {K[0,1]:.4f}")  # < 1.0

Architecture¶

Classical Data → Feature Map → PQC (trainable) → Measurement → Prediction
    [x₁, x₂]     RY(x_i)     RY(θ_i) + CX       |ψ⟩→P(0)     0 or 1

Feature Map: Encodes data into quantum state
Ansatz (PQC): Trainable rotation + entangling layers
Gradient: Parameter-shift rule (exact, quantum-native)
Optimizer: Gradient descent with configurable learning rate

QML vs Classical ML¶

Feature	Classical (sklearn)	Quanta QML
Feature space	d dimensions	2^n dimensions
Kernel trick	Polynomial, RBF	Quantum kernel
Training	SGD, Adam	Parameter-shift
Expressibility	Fixed	Exponential
Current advantage	Large datasets	Small, structured data

Try It Yourself¶

Try n_layers=4 — does accuracy improve?
Compare AngleFeatureMap vs ZZFeatureMap for the same data
Use QuantumKernel with 3 features and 3 qubits

What's Next¶

→ 07 — Error Correction: Protect your quantum computation