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Which Encoding Should I Use?

This page helps you narrow down the right encoding by walking through the key decision factors. Answer the questions below to arrive at a recommendation.

Step 1: What Kind of Data?

Data Type Recommended Encodings
Continuous features (floats) Angle, IQP, ZZ, Data Re-uploading, Trainable
Binary / categorical Basis Encoding
High-dimensional (>16 features) Amplitude Encoding (qubit-efficient) or Angle (simple)
Data with known symmetry SO(2), Cyclic, Swap Equivariant

Step 2: What Is Your Priority?

Accuracy

Choose encodings with high expressibility and entanglement capability:

  • IQP Encoding — provably hard kernel, excellent for classification
  • Data Re-uploading — universal approximation with enough layers
  • ZZ Feature Map — strong pairwise feature interactions

Trainability

Choose shallow encodings with limited entanglement:

  • Angle Encoding — no entanglement, no barren plateaus
  • Hardware Efficient — shallow, tunable depth
  • Trainable Encoding — learnable parameters, controllable expressibility

Hardware Compatibility

Choose low-depth encodings with linear connectivity:

  • Angle Encoding — depth 1, no two-qubit gates
  • IQP (linear entanglement) — O(n) CNOTs instead of O(n^2)
  • Hardware Efficient — designed for native gate sets

Qubit Efficiency

  • Amplitude Encoding — log(n) qubits for n features (but exponential depth)

Step 3: Constraints

Constraint Avoid Prefer
< 10 qubits available Angle with many features Amplitude, or reduce features
Noisy hardware (high error rates) Deep circuits (IQP full, Amplitude) Angle, Hardware Efficient
Need classical baseline comparison Simulable encodings (can't show advantage) IQP, ZZ (non-simulable)
Training budget is small High-rep entangling encodings Angle, shallow Data Re-uploading

Decision Matrix

Encoding Expressibility Trainability NISQ-Friendly Quantum Advantage
Angle Low High Yes No
Amplitude Maximal Moderate No Possible
Basis Minimal High Yes No
IQP High Moderate Moderate Yes
ZZ Feature Map High Moderate Moderate Yes
Pauli Feature Map High Moderate Moderate Depends
Data Re-uploading High Moderate Yes (if shallow) Possible
Hardware Efficient Moderate High Yes Possible
Equivariant Targeted High Moderate On symmetric data

Still Unsure?

Use the programmatic recommender:

from encoding_atlas.guide import recommend_encoding

rec = recommend_encoding(
    n_features=4,
    n_samples=500,
    task='classification',
    hardware='simulator',
    priority='accuracy'
)
print(rec.encoding_name, '-', rec.explanation)

Or see the Decision Flowchart for a visual walkthrough.