QuProFS: An Evolutionary Training-free Approach to Efficient Quantum Feature Map Search

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 parameterised quantum circuits. To address these issues, we propose an evolutionary training-free quantum architecture search (QAS) framework that employs circuit-based heuristics focused on trainability, hardware robustness, generalisation 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 our approach on classification tasks (using quantum support vector machine) across diverse datasets using both artificial and quantum-generated datasets. Our approach demonstrates competitive accuracy on both simulators and real quantum hardware, surpassing state-of-the-art QAS methods in terms of sampling efficiency and achieving up to a 2x speedup in architecture search runtime.