Quantum feature encoding optimization

TL;DR

Quantum Feature Encoding Optimization (QFEO) introduces a general framework to boost quantum machine learning by optimizing how input features are preprocessed before encoding into a fixed quantum feature map. By applying classical data manipulations—selection, weighting, and ordering—driven by Bayesian optimization and cross-validated evaluation, QFEO improves QML performance across diverse datasets and feature-map configurations, both in noiseless simulations and on real quantum hardware. The approach is compatible with projected quantum feature maps and exploits a PQFM pipeline to produce enriched classical features for downstream classifiers, demonstrating practical feasibility on up to 100-qubit hardware with meaningful gains. These results underscore the importance of encoding strategy density and data preprocessing in near-term quantum learning tasks and point to broader future work in richer manipulations, error mitigation, and comparing quantum-encoded pipelines against classical baselines.

Abstract

Quantum Machine Learning (QML) holds the promise of enhancing machine learning modeling in terms of both complexity and accuracy. A key challenge in this domain is the encoding of input data, which plays a pivotal role in determining the performance of QML models. In this work, we tackle a largely unaddressed aspect of encoding that is unique to QML modeling -- rather than adjusting the ansatz used for encoding, we consider adjusting how data is conveyed to the ansatz. We specifically implement QML pipelines that leverage classical data manipulation (i.e., ordering, selecting, and weighting features) as a preprocessing step, and evaluate if these aspects of encoding can have a significant impact on QML model performance, and if they can be effectively optimized to improve performance. Our experimental results, applied across a wide variety of data sets, ansatz, and circuit sizes, with a representative QML approach, demonstrate that by optimizing how features are encoded in an ansatz we can substantially and consistently improve the performance of QML models, making a compelling case for integrating these techniques in future QML applications. Finally we demonstrate the practical feasibility of this approach by running it using real quantum hardware with 100 qubit circuits and successfully achieving improved QML modeling performance in this case as well.

Figures (26)

• Figure 1: Quantum Kernels (blue path) and Variational Quantum Classifiers (orange path) expect static initial encodings $U_{enc}(x)$. Our contribution is to optimize the way we encode the features in the initial feature map (e.g., by changing the order of the features over $n$ iterations)
• Figure 2: We report four examples to visualize different feature encoding manipulations considering a generic feature map. We define $\alpha$ as a multiplicative factor applied to all features (a common hyper parameter in QML methods). In these examples, we assume to have input data with 12 features $\{x_0, \dots, x_{11}\}$ to encode. In Feature Weighting, $w_i$ is the scaling factor applied to the i-th feature. Note that combination of manipulations are also valid, e.g., feature weighting and ordering.
• Figure 3: Representative QML model schema. Feature map $U$ is used to encode input data $x$ into quantum registers. Then, measurements of expectation values for Pauli X, Y, and Z observables are performed to extract a new set of real-valued classical features that are used to fit a classifier $C$.
• Figure 4: QFEO framework phases overview. We illustrate feature selection as the data manipulation technique where the gray features are the ones that are used to fit the QML model, based on the input weights $w$. We apply grids search with cross-validation (GridSearchCV) to search for the best QML model classifier $C$ among $k$ different sets of hyperparameters $\mathcal{H}_k$, and estimate generalization / test performance with a different cross-validation evaluation (KFoldCV).
• Figure 5: Example of 2-qubits Separate Entangled feature map. We define $\alpha$ as the Pauli rotation factor and $x_i$ is the $i$-th feature, $i=0, ..., 11$.