Decision Flowchart

A visual guide to selecting a quantum encoding. Start at the top and follow the arrows — every one of the 16 encodings is reachable.

This flowchart mirrors EncodingDecisionTree.decide()

The flowchart below is a 1:1 representation of the deterministic decision tree implemented in encoding_atlas.guide.decision_tree. For the scored recommendation engine (which returns alternatives and confidence), see Recommendation Architecture.

---

The Flowchart

flowchart TD
    START([Start]) --> L1{"<b>Level 1</b><br/>What is your data type?"}

    L1 -- "binary / discrete" --> BASIS([Basis Encoding])
    L1 -- "continuous" --> L2{"<b>Level 2</b><br/>Does your data have<br/>a known symmetry?"}

    L2 -- "rotation<br/>(exactly 2 features)" --> SO2([SO2 Equivariant])
    L2 -- "cyclic" --> CYCLIC([Cyclic Equivariant])
    L2 -- "permutation_pairs<br/>(even features)" --> SWAP([Swap Equivariant])
    L2 -- "general<br/>(heuristic)" --> SYMI([Symmetry-Inspired])
    L2 -- "none" --> L3{"<b>Level 3</b><br/>Do you want trainable<br/>encoding parameters?"}

    L3 -- "yes" --> TRAIN([Trainable Encoding])
    L3 -- "no" --> L4{"<b>Level 4</b><br/>What is the<br/>problem structure?"}

    L4 -- "combinatorial / graph" --> QAOA([QAOA-Inspired])
    L4 -- "physics simulation" --> HAM([Hamiltonian Encoding])
    L4 -- "time series / periodic" --> DRU_TS([Data Re-uploading])
    L4 -- "none / general" --> L5{"<b>Level 5</b><br/>Do you need specific<br/>feature interactions?"}

    L5 -- "polynomial<br/>(no entanglement)" --> HOA([Higher-Order Angle])
    L5 -- "custom Pauli strings" --> PFM([Pauli Feature Map])
    L5 -- "none" --> L6{"<b>Level 6</b><br/>What is your<br/>optimisation priority?"}

    L6 -- "speed" --> ANGLE([Angle Encoding])
    L6 -- "noise_resilience" --> HWE([Hardware Efficient])
    L6 -- "trainability" --> DRU_PR([Data Re-uploading])
    L6 -- "accuracy" --> L7{"<b>Level 7</b><br/>How many features?"}

    L7 -- "≤ 4" --> IQP([IQP Encoding])
    L7 -- "5 – 8" --> ZZ([ZZ Feature Map])
    L7 -- "> 8" --> AMP([Amplitude Encoding])

    classDef green  fill:#388e3c,stroke:#1b5e20,color:#fff
    classDef blue   fill:#1976d2,stroke:#0d47a1,color:#fff
    classDef purple fill:#7b1fa2,stroke:#4a148c,color:#fff
    classDef yellow fill:#f9a825,stroke:#f57f17,color:#fff
    classDef orange fill:#f57c00,stroke:#e65100,color:#fff
    classDef brown  fill:#5d4037,stroke:#3e2723,color:#fff
    classDef pink   fill:#c2185b,stroke:#880e4f,color:#fff

    class BASIS,ANGLE,HWE green
    class SO2,CYCLIC,SWAP,SYMI blue
    class TRAIN purple
    class QAOA,HAM yellow
    class DRU_TS,DRU_PR orange
    class HOA,PFM brown
    class IQP,ZZ,AMP pink

Data Re-uploading has two paths

data_reuploading is reachable via two distinct routes: problem_structure="time_series" (Level 4) and priority="trainability" (Level 6). All other encodings have exactly one path.

---

Colour Legend

Colour	Category	Encodings
Green	Simple / shallow	Basis, Angle, Hardware Efficient
Blue	Symmetry-aware	SO2, Cyclic, Swap Equivariant, Symmetry-Inspired
Purple	Learnable	Trainable
Yellow	Domain-specific	QAOA-Inspired, Hamiltonian
Orange	Deep / expressive	Data Re-uploading
Brown	Feature interaction	Higher-Order Angle, Pauli Feature Map
Pink	Accuracy / kernel	IQP, ZZ Feature Map, Amplitude

---

Quick Reference Table

Level	Condition	Encoding	Key Tradeoff
1	Binary / discrete data	Basis	Simple but limited to discrete inputs
2	Rotational symmetry (2 features)	SO2 Equivariant	Rigorous 2D rotation equivariance
2	Cyclic symmetry	Cyclic Equivariant	Ring-topology Z_n shift symmetry
2	Permutation pairs (even features)	Swap Equivariant	Rigorous S_2 pair-swap symmetry
2	General symmetry	Symmetry-Inspired	Heuristic symmetry inductive bias
3	Trainable parameters desired	Trainable	Learnable but needs optimisation budget
4	Combinatorial / graph problem	QAOA-Inspired	Cost-mixer structure for optimisation
4	Physics simulation	Hamiltonian	Trotterised time evolution, deep circuits
4	Time series / periodic data	Data Re-uploading	Universal approximation, deep circuits
5	Polynomial interactions (no entanglement)	Higher-Order Angle	Order-k products, classically simulable
5	Custom Pauli string rotations	Pauli Feature Map	Flexible but complex to configure
6	Priority = speed	Angle	O(1) depth, no entanglement, no barren plateaus
6	Priority = noise resilience	Hardware Efficient	Native gates, low CNOT count
6	Priority = trainability	Data Re-uploading	Universal approximation via repeated encoding
7	Priority = accuracy, ≤ 4 features	IQP	Provably hard kernels, full entanglement
7	Priority = accuracy, 5–8 features	ZZ Feature Map	Standard pairwise feature interactions
7	Priority = accuracy, > 8 features	Amplitude	Exponential compression, logarithmic qubits

---

Programmatic Usage

The flowchart above corresponds exactly to EncodingDecisionTree.decide():

from encoding_atlas.guide import EncodingDecisionTree

tree = EncodingDecisionTree()

# Example: continuous data, no symmetry, accuracy priority, 6 features
result = tree.decide(
    data_type="continuous",
    n_features=6,
    priority="accuracy",
)
print(result)  # "zz_feature_map"

For ranked recommendations with confidence scores and alternatives, use the scored recommender instead:

from encoding_atlas.guide import recommend_encoding

rec = recommend_encoding(
    n_features=6,
    priority="accuracy",
    hardware="simulator",
)
print(rec.encoding_name)   # Top pick
print(rec.alternatives)    # Up to 3 runners-up
print(rec.confidence)      # 0.50 – 0.95

Want the full details?

See Recommendation Architecture for the complete scoring breakdown, weight hierarchy, confidence mapping, and worked examples.