Threshold-Based Adaptive Quantum Input Encoding for Variational Optimization of Weighted Max-Cut Problem

Abstract

In variational quantum optimization methods, the manner in which classical data are embedded into the quantum circuit significantly influences the representational capacity and solution behavior of the model. In the literature, this aspect is generally considered a secondary component. In this study, the effect of a threshold-based adaptive quantum encoding approach is analyzed using the NP-hard max-cut problem. The proposed method transforms normalized node-based features into quantum rotations through a data-sensitive angle mapping governed by a threshold value. Experimental results indicate that the adaptive encoding variant with a global threshold value of $(\mathbf{t}=\mathbf{0. 7 5})$ achieves a higher performance in terms of the average approximation ratio compared to standard encoding methods. These findings demonstrate that input encoding should be considered a critical modeling component in variational quantum optimization.