Solving optimization problems using quantum computing has recently received significant attention due to its potential to enhance computational speed by leveraging quantum mechanics. One promising framework involves integrating quantum computing with machine learning techniques, commonly referred to as quantum machine learning (QML) [1]. This approach combines the computational advantages of quantum physics with the pattern recognition capabilities of machine learning models. Among the QML models, the parameterized quantum circuit [2] is the most fundamental and widely recognized, featuring trainable parameters analogous to the weights in classical neural networks. Indeed, QML has demonstrated robust performance across various applications [3], but its potential in computer-aided engineering remains largely unexplored. In fact, the application of quantum machine learning to structural optimization remains limited, especially for nonlinear problems. In this study, we explore a novel framework that utilizes QML to address topology optimization with nonlinearity challenges for continuum structures. The parameterized quantum circuits are trained by optimizing a loss function using precomputed optimal structures provided during an offline training phase, analogous to the training process in classical neural networks. To evaluate its performance, the proposed QML-assisted topology optimization framework is applied to designing optimal topologies of continuum structures under various boundary conditions. The results reveal that the framework successfully predicts optimal topologies, demonstrating its potential to advance QML techniques for nonlinear topology optimization.