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Design note: QuantumSVM feature_map="auto" (Qmes-style spike)

Status: experimental feature included in SuperQuantX 0.3.0. Inspired by Qmes (arXiv:2609.04652).

Paper scope and limits (read before demoing)

The Qmes results in arXiv:2609.04652 hold only within this scope:

  • 7 circuits: a fixed pool (unit, SRx, RY, HERx, RY_CX, ZFM, HD), implemented in the bundled Qsun simulator, not in SuperQuantX backends.
  • 4 qubits: every dataset is reduced by PCA to at most 4 components and rescaled before kernel evaluation, so rankings describe 4-qubit circuits.
  • Noiseless simulation: all circuit scores come from noiseless state-vector simulation. Hardware noise and noise models are not modelled, so a recommendation says nothing about performance on real QPUs.
  • Supervised tabular data only (labels required), meta-features computed on at most 600 subsampled points, fixed non-trainable kernels.
  • Reported gains (2.2x lower mean regret for classification, 4.2x for regression versus a non-adaptive baseline) are leave-one-out results on the authors' 105 classification and 86 regression benchmark datasets.

SuperQuantX maps the Qmes circuit names onto its own, differently shaped feature maps (see below), so the paper's regret numbers do not transfer directly to SuperQuantX kernels. Treat feature_map="auto" as a heuristic starting point, not a validated optimum.

Installing Qmes (optional)

Qmes is an optional runtime import, not a package extra. It is not published on PyPI, and PyPI (and hatchling) reject direct git references in extras, so SuperQuantX does not declare it as a dependency. Install it manually if you want the pre-trained recommender:

pip install git+https://github.com/tungduy1704/Qmes

Without Qmes, feature_map="auto" (mode auto) uses the built-in classical heuristic. Tests run without Qmes installed.

Why

QuantumSVM performance depends strongly on the encoding circuit. Exhaustive kernel evaluation of every candidate is expensive. Qmes shows that classical dataset complexity features can rank encoding circuits without quantum evaluation at inference time. This spike adds a practical feature_map="auto" path that recommends a name from SuperQuantX's existing feature-map registry.

What we adopted

  1. Registry (utils/feature_map_registry.py) Canonical names: ZZFeatureMap, PauliFeatureMap, AmplitudeMap, AngleEncoding, ZFeatureMap. Manual string aliases still work.

  2. Qmes mapping (QMES_TO_SUPERQUANTX)

Qmes pool SuperQuantX registry Rationale
unit AmplitudeMap Amplitude / square-root style embedding
SRx AngleEncoding Separable single-qubit rotations
RY AngleEncoding Separable RY angle encoding
HERx PauliFeatureMap Hardware-efficient rotations + CX
RY_CX PauliFeatureMap Angle + linear CX
ZFM ZFeatureMap Separable Z rotations
HD ZZFeatureMap High-dim / entangling analogue
  1. Selector (utils/feature_map_auto.py)
  2. mode="auto": try Qmes if installed, else heuristic.
  3. mode="qmes": require the optional Qmes package (runtime import only).
  4. mode="heuristic": local meta-features only (no problexity, no quantum).

  5. Heuristic uses sample/feature ratio, mean |correlation|, class imbalance, and a cheap logistic-regression separability proxy.

  6. QuantumSVM

  7. feature_map="auto" or None resolves at fit() time.
  8. Stores selected_feature_map_ and feature_map_recommendation_.

  9. Existing manual strings/objects are unchanged.

  10. Backends Simulator / PennyLane / Qiskit / Cirq create_feature_map recognize AngleEncoding and ZFeatureMap through the shared feature-map implementation.

What we deferred

  • Full Qmes circuit pool implementations (unit, SRx, HERx, RY_CX, HD gate schedules, Qsun backend, fixed 4-qubit PCA pipeline).
  • Shipping or re-training a SuperQuantX-native pairwise OvO recommender on our own meta-dataset and backends.
  • Problexity's full 22-d / 12-d complexity vectors in the default heuristic.
  • Noise-aware or hardware-aware recommendation.
  • Regression-task auto selection wired into a QuantumSVR (QSVM remains classification-focused).
  • Changing the default constructor value away from ZZFeatureMap (auto is opt-in).

Circuit-pool gaps

Qmes evaluates seven Qsun encodings with a shared 4-qubit PCA + MinMax preprocess. SuperQuantX backends implement a smaller, differently shaped set. Closest-name mapping is approximate:

  • Exact Qmes unit / HD gate lists are not reproduced.
  • AmplitudeMap is a registry candidate but is not implemented by the shared backends. Automatic selection chooses the next implemented map from the ranking and records unavailable_feature_map in the recommendation details. Explicit requests raise an error.
  • Entanglement patterns (linear CX vs ISWAP brickwork) differ.
  • Recommendation quality of the heuristic is unvalidated against Qmes regret.

How to try

from sklearn.datasets import make_classification
from superquantx.algorithms import QuantumSVM

X, y = make_classification(n_samples=40, n_features=4, n_informative=3, random_state=0)
qsvm = QuantumSVM(backend="simulator", feature_map="auto", shots=100)
qsvm.fit(X, y)
print(qsvm.selected_feature_map_)
print(qsvm.feature_map_recommendation_)

Optional Qmes path:

pip install git+https://github.com/tungduy1704/Qmes

qsvm = QuantumSVM(
    backend="simulator",
    feature_map="auto",
    auto_feature_map_mode="qmes",
)

Follow-ups

  1. Expand the registry with first-class Qmes-like encodings (or adapters).
  2. Build a SuperQuantX meta-dataset on simulator kernels and train a pairwise recommender (or fine-tune Qmes with registered SQX circuits).
  3. Expose recommend_feature_map in the CLI / docs tutorials.
  4. Add regression auto-selection once a Quantum kernel regressor lands.
  5. Benchmark heuristic vs Qmes vs fixed ZZFeatureMap on shared datasets.