Digitized Counterdiabatic Quantum Feature Extraction

TL;DR

This work tackles the challenge of enriching feature representations for data-driven tasks by leveraging quantum dynamics. It proposes a Hamiltonian-based quantum feature extraction framework that embeds classical data into $k$-local spin-glass Hamiltonians and uses counterdiabatic driving to generate expressive feature maps from low- and high-order observables. Evaluated on molecular toxicity and breast-tumor detection with IBM's Kingston device, the approach yields consistent improvements over classical baselines, and SHAP analyses reveal that quantum-derived features often dominate the model decisions. The results demonstrate a practical, hardware-efficient pathway for near-term quantum-assisted learning, where quantum features complement classical preprocessing to enhance performance across diverse datasets.

Abstract

We introduce a Hamiltonian-based quantum feature extraction method that generates complex features via the dynamics of $k$-local many-body spins Hamiltonians, enhancing machine learning performance. Classical feature vectors are embedded into spin-glass Hamiltonians, where both single-variable contributions and higher-order correlations are represented through many-body interactions. By evolving the system under suitable quantum dynamics on IBM digital quantum processors with 156 qubits, the data are mapped into a higher-dimensional feature space via expectation values of low- and higher-order observables. This allows us to capture statistical dependencies that are difficult to access with standard classical methods. We assess the approach on high-dimensional, real-world datasets, including molecular toxicity classification and image recognition, and analyze feature importance to show that quantum-extracted features complement and, in many cases, surpass classical ones. The results suggest that combining quantum and classical feature extraction can provide consistent improvements across diverse machine learning tasks, indicating a reliable level of early quantum usefulness for near-term quantum devices in data-driven applications.

Figures (6)

• Figure 1: Illustration of quantum feature extraction using multiple quantum dynamics for the molecular toxicity case. (a) Tabular dataset $X$, from which samples and classical correlations are selected. (b) The extracted information from $X$ is encoded into the local fields and higher-order coefficients of spin Hamiltonians (see Eq. \ref{['eq:encoding_hamiltonian']}), differing in the order of interaction terms. (c) Local magnetizations and quantum correlations are measured from the two circuits and concatenated, yielding the quantum-extracted features.
• Figure 2: Protocol for the image classification case, combining classical and quantum feature extraction methods. (a) Image-based dataset, where conventional feature extraction techniques are used to construct a tabular dataset $X$, from which samples and classical correlations are selected (as in Fig. \ref{['fig:schem_tox']}). (b) The extracted information from $X$ is encoded into the local fields and two-body coefficients of a spin Hamiltonian (see Eq. \ref{['eq:encoding_hamiltonian']}). (c) Local magnetizations and quantum correlations are measured and concatenated, forming the quantum-extracted features.
• Figure 3: Performance and feature-importance analysis for (a) molecular toxicity classification and (b) breast tumor detection. Left: cross-validated (5×5) Gradient Boosting performance across metrics using different sets of classical and quantum-extracted features, as well as their SHAP-based combination. Right: SHAP importance of the features selected as most relevant by the tree explainer.
• Figure 4: Illustration of the (b) embedded (logical) problem compared to the heavy-hexagonal topology extracted from the (a) native connections of IBM Kingston.
• Figure 5: Visualization of a 3-uniform hypergraph representing all three-body interactions among spin variables. Each triangular hyperedge corresponds to a third-order term in the encoded spin-glass Hamiltonian, where the presence and strength of a hyperedge encode the magnitude of the associated third-order mutual information between the connected variables. This hypergraph structure forms the basis for constructing higher-order energy landscapes that capture nonlinear correlations beyond pairwise couplings.