QuProFS: an evolutionary training-free approach to efficient quantum feature map search

Abstract The quest for effective quantum feature maps for data encoding presents significant challenges, particularly due to the flat training landscapes and lengthy training processes associated with parameterized quantum circuits. To address the gap between training-free search evaluation and downstream task performance, we propose Quantum Proxy-assisted Feature Search (QuProFS) framework that employs circuit-based heuristics focused on trainability, hardware robustness, generalization ability, expressivity, complexity, and kernel-target alignment. By ranking circuit architectures with various proxies, we reduce evaluation costs and incorporate hardware-aware circuits to enhance robustness against noise. We evaluate QuProFS on binary classification tasks using a quantum support vector machine on nine benchmark datasets, including Breast Cancer, MNIST-2, Fashion-MNIST-2, Coset-10, Two Curves, Hidden Manifold, Linearly Separable, Bars-and-Stripes, and Hyperplane, using both quantum simulators and IBM Quantum hardware. Compared with existing quantum architecture search methods, QuProFS achieves the highest accuracy on the majority of benchmark datasets while reducing architecture search time by up to 2 × . Furthermore, QuProFS achieves classification performance comparable to strong classical machine learning baselines on several benchmark datasets, demonstrating an efficient and scalable strategy for quantum feature map optimization.