Quantum Machine Learning (QML) blends quantum computing with classical ML to unlock speed-ups in optimization, sampling, and high-dimensional learning.
This post covers core QML algorithms with practical Python/Qiskit examples so developers can start experimenting today.

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🔹 1. Quantum Support Vector Machines (QSVM)

QSVMs use quantum kernel estimation, which allows efficient mapping of classical data into extremely high-dimensional Hilbert spaces.

🧪 Qiskit Example — Quantum Kernel

from qiskit import BasicAer
from qiskit.utils import QuantumInstance
from qiskit_machine_learning.kernels import QuantumKernel
from qiskit.circuit.library import ZZFeatureMap

feature_map = ZZFeatureMap(feature_dimension=2, reps=2)
quantum_kernel = QuantumKernel(feature_map=feature_map,
quantum_instance=QuantumInstance(BasicAer.get_backend('statevector_simulator')))

kernel_matrix = quantum_kernel.evaluate(x_vec=[[0, 1]], y_vec=[[1, 0]])
print(kernel_matrix)

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🔹 2. Quantum Neural Networks (QNNs)

QNNs use variational quantum circuits trained with classical optimizers in a hybrid loop.

Qiskit Example — A Simple VQC Model

from qiskit import Aer
from qiskit.algorithms.optimizers import COBYLA
from qiskit_machine_learning.neural_networks import TwoLayerQNN

backend = Aer.get_backend("statevector_simulator")

qnn = TwoLayerQNN(num_inputs=2, num_qubits=2, quantum_instance=backend)
optimizer = COBYLA()

def objective(x):
return qnn.forward(x)[0]

result = optimizer.minimize(objective, x0=[0.1, 0.5])
print(result)

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🔹 3. Quantum k-Means Clustering

Quantum k-means speeds up distance calculations using superposition and amplitude encoding.

Sketch (high-level qiskit pseudocode)

from qiskit_machine_learning.algorithms import QSVM

Quantum k-means isn't fully standardized yet, many researchers use quantum kernels.

Distances can be computed via swap tests or inner-product circuits.

(If you want, I can include a custom quantum distance circuit.)

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🔹 4. Quantum PCA (qPCA)

Quantum PCA uses quantum phase estimation (QPE) to extract principal components of a density matrix.

Minimal Example (Qiskit)

from qiskit import QuantumCircuit
from qiskit.circuit.library import QFT

n_qubits = 3
qc = QuantumCircuit(n_qubits)

Example: QPE structure (simplified)

qc.h(range(n_qubits - 1))
qc.append(QFT(num_qubits=n_qubits-1), range(n_qubits-1))

qc.draw('mpl')

(This acts as the backbone for qPCA implementations.)

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🔹 5. Quantum Generative Adversarial Networks (QGANs)

QGANs combine:

A quantum generator

A classical OR quantum discriminator

Qiskit Example — QGAN Training Loop

from qiskit_machine_learning.algorithms import QGAN
from qiskit import BasicAer

real_data = [[0.1], [0.9]]
qgan = QGAN(real_data=real_data,
num_qubits=1,
batch_size=20,
quantum_instance=BasicAer.get_backend("qasm_simulator"))

qgan.run()

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🔹 6. QAOA and VQE (Optimization Algorithms)

Many ML tasks (loss minimization, feature selection, clustering) are optimization problems.
QAOA and VQE use quantum circuits to optimize energy landscapes.

Qiskit Example — Simple VQE

from qiskit.algorithms import VQE
from qiskit.algorithms.optimizers import SLSQP
from qiskit.circuit.library import TwoLocal
from qiskit.primitives import Estimator
from qiskit.quantum_info import SparsePauliOp

hamiltonian = SparsePauliOp.from_list([("ZZ", 1)])
ansatz = TwoLocal(2, "ry", "cx", reps=2)
optimizer = SLSQP()

vqe = VQE(Estimator(), ansatz, optimizer)
result = vqe.compute_minimum_eigenvalue(operator=hamiltonian)

print(result.eigenvalue)

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🧠 Why QML Matters for Developers

✔ Exponential feature mapping
✔ Faster optimization in ML workflows
✔ Parallelism via superposition
✔ More expressive generative models
✔ Useful for chemistry, finance, logistics, and material science

Quantum advantage in ML is still emerging, but developers experimenting today with Qiskit, PennyLane, Cirq, or AWS Braket will lead the next wave of AI innovation.

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🚀 Final Thoughts

Quantum ML is not just “faster computing” — it’s a fundamentally new computational paradigm.