Dimensionality Reduction¶

Current quantum hardware is limited to tens or hundreds of qubits. Most real-world datasets have far more features. Reduction brings your data into a range that hardware can handle.

Why it matters¶

Encoding	Qubits needed for d features
Angle	d qubits
Amplitude	\(\log_2(d)\) qubits
Basis	d qubits
IQP	d qubits

If your dataset has 512 features and your backend has 127 qubits, angle encoding is infeasible without reduction.

PCA¶

Good general-purpose default. n_components can be an integer (exact) or float (variance fraction, e.g. 0.95).

import quprep as qd

pipeline = qd.Pipeline(
    reducer=qd.PCAReducer(n_components=8),
    encoder=qd.AngleEncoder(),
)
result = pipeline.fit_transform("data.csv")

# Access explained variance after fit
print(pipeline.reducer.explained_variance_ratio_)

LDA¶

Maximises class separability. Research shows LDA outperforms PCA for quantum classification tasks. Requires class labels. Maximum components: n_classes − 1.

import quprep as qd

pipeline = qd.Pipeline(
    reducer=qd.LDAReducer(n_components=4, labels=y),
    encoder=qd.AngleEncoder(),
)
result = pipeline.fit_transform("data.csv")

# Access explained variance after fit
print(pipeline.reducer.explained_variance_ratio_)

Spectral (DFT)¶

Row-wise FFT — keeps the first n_components frequency magnitudes. Outputs are always ≥ 0. Best for time-series and signal data.

import quprep as qd

pipeline = qd.Pipeline(
    reducer=qd.SpectralReducer(n_components=8),
    encoder=qd.AngleEncoder(),
)

t-SNE¶

Preserves local structure. Best suited to 2–3 qubit circuits and visualization tasks.

import quprep as qd

reducer = qd.TSNEReducer(n_components=2, perplexity=30)

Warning

t-SNE requires perplexity < n_samples. For small datasets use a lower perplexity.

UMAP¶

pip install umap-learn

Faster than t-SNE and scales to large datasets. Preserves both local and global structure.

import quprep as qd

reducer = qd.UMAPReducer(n_components=4)

Raises ImportError with install hint if umap-learn is not installed.

Hardware-aware reduction¶

Automatically calculates the qubit budget for a target backend and reduces to fit. No manual calculation needed.

import quprep as qd

# By backend name
pipeline = qd.Pipeline(
    reducer=qd.HardwareAwareReducer(backend="ibm_brisbane"),
    encoder=qd.AngleEncoder(),
)

# By qubit count
pipeline = qd.Pipeline(
    reducer=qd.HardwareAwareReducer(backend=16),
    encoder=qd.AngleEncoder(),
)

Supported backends: ibm_brisbane (127), ibm_kyiv (127), ibm_torino (133), ionq_harmony (11), quantinuum_h1 (20), and more. Pass an integer to specify any qubit count directly.

References

Mancilla, J., & Pere, C. (2022). A preprocessing perspective for quantum machine learning classification advantage in finance using NISQ algorithms. Entropy, 24(11), 1656. doi:10.3390/e24111656