BVQC: A Backdoor-style Watermarking Scheme for Variational Quantum Circuits

Variational Quantum Circuits (VQCs) have emerged as a powerful quantum computing paradigm, demonstrating a scaling advantage for problems intractable for classical computation. As VQCs require substantial resources and specialized expertise for their design, they represent significant intellectual properties (IPs). However, existing quantum circuit watermarking techniques suffer from two primary drawbacks: (1) watermarks can be removed during re-compilation of the circuits, and (2) these methods significantly increase task loss due to the extensive length of the inserted watermarks across multiple compilation stages. To address these challenges, we propose BVQC, a backdoor-based watermarking technique for VQCs that preserves the original loss in typical execution settings, while deliberately increasing the loss to a predefined level during watermark extraction. Additionally, BVQC employs a grouping algorithm to minimize the watermark task's interference with the base task, ensuring optimal accuracy for the base task. BVQC retains the original compilation workflow, ensuring robustness against re-compilation. Our evaluations show that BVQC greatly reduces Probabilistic Proof of Authorship (PPA) changes by 9.89e-3 and ground truth distance (GTD) by 0.089 compared to prior watermarking technologies.