Quantum feature-map learning with reduced resource overhead

TL;DR

The paper introduces Q-FLAIR, a principled approach to learn quantum feature-maps with dramatically reduced quantum-resource overhead by offloading the core learning steps to classical computation via analytic reconstructions. By greedily growing the ansatz and simultaneously optimizing gate choice, feature selection, and weight parameters, Q-FLAIR achieves high-accuracy QNN and QSVM models while keeping circuits shallow and hardware-friendly. Empirical results on simulated benchmarks and real IBM hardware show strong performance on high-dimensional data (up to $d=784$) and full-resolution MNIST (digits 3 vs 5), with QNNs reaching over $90\%$ test accuracy and QSVMs exceeding $80\%$ across tasks. This work demonstrates that rethinking feature-map learning as resource-aware, analytic, data-driven design can make quantum machine learning feasible on near-term devices and real-world problems.

Abstract

Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature maps, which embed classical data into the state space of qubits. We introduce Quantum Feature-Map Learning via Analytic Iterative Reconstructions (Q-FLAIR), an algorithm that reduces quantum resource overhead in iterative feature-map circuit construction. It shifts workloads to a classical computer via partial analytic reconstructions of the quantum model, using only a few evaluations. For each probed gate addition to the ansatz, the simultaneous selection and optimization of the data feature and weight parameter is then entirely classical. Integrated into quantum neural network and quantum kernel support vector classifiers, Q-FLAIR shows state-of-the-art benchmark performance. Since resource overhead decouples from feature dimension, we train a quantum model on a real IBM device in only four hours, surpassing 90% accuracy on the full-resolution MNIST dataset (784 features, digits 3 vs 5). Such results were previously unattainable, as the feature dimension prohibitively drives hardware demands for fixed and search costs for adaptive ansätze. By rethinking feature-map learning beyond black-box optimization, this work takes a concrete step toward enabling quantum machine learning for real-world problems and near-term quantum computers.

Figures (9)

• Figure 1: Schematic comparison of traditional quantum feature-map learning and Q-FLAIR. The figure illustrates the distribution of computational workloads between quantum (violet) and classical (green) computers. Multiple subroutines that are repeatedly executed on a quantum computer in traditional approaches are shifted to classical computers in Q-FLAIR. By retrieving partial analytic reconstructions of the quantum model from only a few quantum evaluations (blue box), Q-FLAIR reduces the resource overhead of quantum feature-map learning.
• Figure 2: QNN performance benchmark on four different datasets. Top panels: accuracy over the number of gates appended to the feature-map circuit by Q-FLAIR, where each point corresponds to the QNN with the intermediate circuit obtained after each gate addition. Gray curves show training accuracy, colored curves show test accuracy. Bottom panels: the corresponding feature-map circuits built gate by gate with Q-FLAIR. Each rectangle denotes a gate (single- or two-qubit), with coloring indicating its parameter value between -1.0 (black) and 1.0 (color).
• Figure 3: QSVM performance benchmark on four different datasets. Top panels: accuracy over the number of gates appended to the feature-map circuit by Q-FLAIR, where each point corresponds to the QSVM with the intermediate circuit obtained after each gate addition. Gray curves show training accuracy, colored curves show test accuracy. Bottom panels: the corresponding feature-map circuits built gate by gate with Q-FLAIR. Each rectangle denotes a gate (single- or two-qubit), with coloring indicating its parameter value between -1.0 (black) and 1.0 (color).
• Figure 4: Comparison of Q-FLAIR with traditional feature-map learning on MNIST (digits 3 vs 5). Accuracies are shown for MNIST PCA (purple) and pixel (light to dark green) variants. Solid lines show Q-FLAIR results, while dashed lines correspond to the traditional feature-map learning without analytic reconstruction. Here, training is terminated after 20.0 gates (Q-FLAIR curves are marked at 20.0 gates for comparison). A random parameter is drawn for each gate–feature combination. Each curve represents the mean over ten independent runs, with shaded bands indicating standard deviations. Traditional learning scales quantum evaluation overhead with feature dimension, exceeding Q-FLAIR by more than two orders of magnitude on MNIST $28\times28$.
• Figure 5: Ablation study of Q-FLAIR optimizations for QNNs on bars & stripes and MNIST PCA. Solid curves (labeled 'Q-FLAIR') correspond to the full algorithm comparison (same as in Fig. \ref{['fig:ann_acc']}). Dotted, dash-dotted, and dashed curves show the effect of replacing gate, feature, or parameter optimization, respectively, by random choices instead of including them in the simultaneous optimization. Each curve represents the mean over ten independent runs, with shaded bands indicating standard deviations.