In short
Each route ends with one value per qubit, scaled to an angle between 0 and π. The RF routes load those angles with one rotation per qubit; PCA uses the entangling ZZFeatureMap. A small trainable circuit follows, tuned by COBYLA.
Each of the reduction methods required different paths for training a VQC:
- Grouped votes: the values from Phase 1 are scaled, then used for angle encoding of a VQC. No reduction technique is needed here since there is already exactly one value per qubit.
- Leaf embedding: the one-hot leaves from Phase 1 are truncated to components using TruncatedSVD, then they are scaled and finally angle encoding happens.
- PCA baseline: all 262,144 standardised features are put through centred PCA to get components, which are then scaled and finally ZZFeatureMap encoding is used. The Random Forest filter is not used, as this is the baseline needed for comparison. The sparse ARPACK solver was used because it centres the data without converting the sparse matrix to a dense one, which was necessary to make PCA run on 262,144 features.
Each value is min-max scaled to and the scaler is only fitted on the training fold. This is so that the values become rotation angles, and this range ensures that they do not wrap around.
The feature map for the RF methods uses angle encoding with one RY rotation per qubit, which gives a product state with no entanglement. For the PCA baseline ZZFeatureMap is used, which has pairwise ZZ phases which entangle the qubits. These feature maps were chosen through validation so that the fairest possible comparison could be made, with each approach using techniques that play to their advantage.
The RealAmplitudes ansatz was used with reverse-linear entanglement, where each qubit is entangled with its neighbour in a chain. The number of repetitions was chosen per condition by validation, so that results are not skewed by poor repetition choices.
For the readout and loss, the class is read by measuring qubit 0, while the loss comes from the cross-entropy over the training fold. The COBYLA optimiser was used with 500 evaluations at most, always starting from seeded random weights. Finally, exact statevector simulation without noise was used.
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