Watermarking Quantum Neural Networks Based on Sample Grouped and Paired Training

Quantum neural networks (QNNs) leverage quantum computing to create powerful and efficient artificial intelligence models capable of solving complex problems significantly faster than traditional computers. With the fast development of quantum hardware technology, such as superconducting qubits, trapped ions, and integrated photonics, quantum computers may become reality, accelerating the applications of QNNs. However, preparing quantum circuits and optimizing parameters for QNNs require quantum hardware support, expertise, and high-quality data. How to protect intellectual property (IP) of QNNs becomes an urgent problem to be solved in the era of quantum computing. We make the first attempt towards IP protection of QNNs by watermarking. To this purpose, we collect classical clean samples and trigger ones, each of which is generated by adding a perturbation to a clean sample, associated with a label different from the ground-truth one. The host QNN, consisting of quantum encoding, quantum state transformation, and quantum measurement, is then trained from scratch with the clean samples and trigger ones, resulting in a watermarked QNN model. During training, we introduce sample grouped and paired training to ensure that the performance on the downstream task can be maintained while achieving good performance for watermark extraction. When disputes arise, by collecting a mini-set of trigger samples, the hidden watermark can be extracted by analyzing the prediction results of the target model corresponding to the trigger samples, without accessing the internal details of the target QNN model, thereby verifying the ownership of the model. Experiments have verified the superiority and applicability of this work.