ZXNet: ZX Calculus-Driven Graph Neural Network Framework for Quantum Circuit Equivalence Checking

Quantum circuit execution often requires transpilation into hardware-compatible instructions, which can significantly alter the original design, making equivalence checking essential. However, existing approaches struggle with scalability and computational overhead. In this paper, we present ZXNet, a transformative framework for quantum circuit equivalence checking using $\mathbf{Z X}$ calculus-based graph abstractions. Leveraging graph neural networks, ZXNet captures complex equivalence patterns by integrating critical local and global circuit features. ZXNet achieves 99.4% validation accuracy, and up to $62 \times$ speedup over state-of-the-art methods, furnishing improvements of 45.83% in scalability, 42.22% in per-qubit verification time, and 5.94% in accuracy, outperforming state-of-the-art approaches.