On Representation Smoothness for Robust Architecture Discovery of Variational Quantum Circuits

Abstract

Discovering diverse, high-performing structured models in mixed discrete–continuous search spaces is a recurring problem in automated and distributional model design. In such settings, the representation used to encode candidate models plays a central role in determining the stability and effectiveness of search. We investigate this issue in the context of variational quantum circuits (VQCs), whose behavior depends jointly on discrete architectural choices and continuous parameters. Existing encodings from the literature enable evolutionary discovery of diverse circuits but induce representational discontinuities, where small changes in the encoding lead to abrupt structural modifications. These discontinuities degrade search stability and robustness as structural sensitivity increases. We analyze the effect of encoding discontinuities on diversity-driven discovery and introduce two representation refinements: a smooth, continuous mechanism for gate selection and a factorized representation that separates structural discovery from continuous parameter optimization. Empirical results across multiple circuit discovery tasks show that a combination of both encoding suggestions ultimately yields smoother representations with higher-quality exploration and lower volatility of discovered models. Our findings identify encoding smoothness as a key design principle for robust discovery in structured model spaces.