Machine Learning

qufin includes quantum machine learning modules for financial applications including classification, generation, and feature extraction.

Quantum Kernel Methods

Quantum kernels compute inner products in a quantum feature space that may capture complex correlations classical kernels miss.

from qufin.ml.kernels import QuantumKernel

kernel = QuantumKernel(
    n_qubits=4,
    feature_map="zz",     # ZZFeatureMap encoding
    n_layers=2,
)

# Compute kernel matrix for training data
K_train = kernel.compute(X_train)

# Use with scikit-learn SVM
from sklearn.svm import SVC
clf = SVC(kernel="precomputed")
clf.fit(K_train, y_train)

K_test = kernel.compute(X_test, X_train)
accuracy = clf.score(K_test, y_test)

Feature Maps

Feature Map	Description	Best For
"zz"	ZZFeatureMap with entangling gates	Correlated features
"pauli"	PauliFeatureMap (customizable Pauli terms)	General purpose
"iqp"	Instantaneous Quantum Polynomial	High-dimensional data

Variational Quantum Classifier (VQC)

A parameterized quantum circuit trained end-to-end for classification tasks.

from qufin.ml.classifiers import VQClassifier

clf = VQClassifier(
    n_qubits=4,
    n_layers=3,
    ansatz="hardware_efficient",
    optimizer="cobyla",
    max_iter=200,
)

clf.fit(X_train, y_train)
predictions = clf.predict(X_test)

Financial Applications

• Credit scoring: Classify loan applicants as default/non-default
• Regime detection: Classify market state as bull/bear/sideways
• Fraud detection: Identify anomalous transactions

Quantum GAN (qGAN)

Quantum generative adversarial network for learning and sampling from probability distributions.

from qufin.ml.qgan import QuantumGAN

qgan = QuantumGAN(
    n_qubits=4,
    generator_layers=3,
    discriminator_hidden=[64, 32],
    learning_rate=0.001,
)

# Train on historical return distribution
qgan.fit(returns_data, epochs=1000, batch_size=64)

# Generate synthetic samples
synthetic_returns = qgan.sample(n_samples=10000)

Use Cases

• Synthetic data generation: Create realistic return distributions for backtesting
• Privacy-preserving data sharing: Share statistical properties without raw data
• Data augmentation: Expand small datasets for training other models

Quantum Reservoir Computing

Uses a fixed quantum circuit as a dynamical reservoir, with only the readout layer trained classically. Computationally cheaper than VQC since the quantum parameters are not optimized.

from qufin.ml.reservoir import QuantumReservoir

reservoir = QuantumReservoir(
    n_qubits=6,
    n_layers=4,
    readout="ridge",  # Ridge regression readout
)

# Time series prediction
reservoir.fit(X_train_seq, y_train)
predictions = reservoir.predict(X_test_seq)

Model Comparison

Model	Trainable Params	Training Cost	Best For
Quantum kernel	0 (kernel only)	O(N^2) kernel matrix	Small datasets, high-dim features
VQC	O(qubits * layers)	Variational optimization	Classification with limited data
qGAN	Generator + discriminator	Adversarial training	Distribution learning
Reservoir	Readout only	Single regression	Time series, fast training

Tips

Start classical, go quantum

Always benchmark against a classical baseline (logistic regression, SVM, XGBoost) first. Quantum ML currently shows advantage primarily on small, highly correlated datasets.

NISQ limitations

Current quantum ML models are limited to 4-10 qubits on real hardware. Use simulators for larger circuits during development.