Estimating the global Lipschitz constant of neural networks is crucial for understanding and improving their robustness and generalization capabilities. However, precise calculations are NP-hard, and current semidefinite programming (SDP) methods face challenges such as high memory usage and slow processing speeds. In this paper, we propose HiQ-Lip, a hybrid quantum-classical hierarchical method that leverages Coherent Ising Machines (CIMs) to estimate the global Lipschitz constant. We tackle the estimation by converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem and implement a multilevel graph coarsening and refinement strategy to adapt to the constraints of contemporary quantum hardware. Our experimental evaluations on fully connected neural networks demonstrate that HiQ-Lip not only provides estimates comparable to state-of-the-art methods but also significantly accelerates the computation process. In specific tests involving two-layer neural networks with 256 hidden neurons, HiQ-Lip doubles the solving speed and offers more accurate upper bounds than the existing best method, LiPopt. These findings highlight the promising utility of small-scale quantum devices in advancing the estimation of neural network robustness.

Data poisoning attacks pose significant threats to machine learning models by introducing malicious data into the training process, thereby degrading model performance or manipulating predictions. Detecting and sifting out poisoned data is an important method to prevent data poisoning attacks. Limited by classical computation frameworks, upcoming larger-scale and more complex datasets may pose difficulties for detection. We introduce the unique speedup of quantum computing for the first time in the task of detecting data poisoning. We present Q-Detection, a quantum-classical hybrid defense method for detecting poisoning attacks. Q-Detection also introduces the Quantum Weight-Assigning Network, which is optimized using quantum computing devices. Experimental results using multiple quantum simulation libraries show that Q-Detection effectively defends against label manipulation and backdoor attacks. The metrics demonstrate that Q-Detection consistently outperforms the baseline methods and is comparable to the state-of-the-art. Theoretical analysis shows that Q-Detection is expected to achieve more than a 20% speedup using quantum computing power.